How to find f(x) - PSAT Math
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If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
If f(x) = _x_2 – 5 for all values x and f(a) = 4, what is one possible value of a?
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Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
Using the defined function, f(a) will produce the same result when substituted for x:
f(a) = _a_2 – 5
Setting this equal to 4, you can solve for a:
_a_2 – 5 = 4
_a_2 = 9
a = –3 or 3
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If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
If the function g is defined by g(x) = 4_x_ + 5, then 2_g_(x) – 3 =
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The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
The function g(x) is equal to 4_x_ + 5, and the notation 2_g_(x) asks us to multiply the entire function by 2. 2(4_x_ + 5) = 8_x_ + 10. We then subtract 3, the second part of the new equation, to get 8_x_ + 7.
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If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
If f(x) = x_2 + 5_x and g(x) = 2, what is f(g(4))?
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First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
First you must find what g(4) is. The definition of g(x) tells you that the function is always equal to 2, regardless of what “x” is. Plugging 2 into f(x), we get 22 + 5(2) = 14.
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f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
f(a) = 1/3(a_3 + 5_a – 15)
Find a = 3.
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Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
Substitute 3 for all a.
(1/3) * (33 + 5(3) – 15)
(1/3) * (27 + 15 – 15)
(1/3) * (27) = 9
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Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
Evaluate f(g(6)) given that f(x) = _x_2 – 6 and g(x) = –(1/2)x – 5
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Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
Begin by solving g(6) first.
g(6) = –(1/2)(6) – 5
g(6) = –3 – 5
g(6) = –8
We substitute f(–8)
f(–8) = (–8)2 – 6
f(–8) = 64 – 6
f(–8) = 58
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If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
If f(x) = |(_x_2 – 175)|, what is the value of f(–10) ?
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If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
If x = –10, then (_x_2 – 175) = 100 – 175 = –75. But the sign |x| means the absolute value of x. Absolute values are always positive.
|–75| = 75
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If f(x)= 2x² + 5x – 3, then what is f(–2)?
If f(x)= 2x² + 5x – 3, then what is f(–2)?
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By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
By plugging in –2 for x and evaluating, the answer becomes 8 – 10 – 3 = -5.
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If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
If f(x) = x² – 2 and g(x) = 3x + 5, what is f(g(x))?
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To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
To find f(g(x) plug the equation for g(x) into equation f(x) in place of “x” so that you have: f(g(x)) = (3x + 5)² – 2.
Simplify: (3x + 5)(3x + 5) – 2
Use FOIL: 9x² + 30x + 25 – 2 = 9x² + 30x + 23
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If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
If f(x)=3x and g(x)=2x+2, what is the value of f(g(x)) when x=3?
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With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
With composition of functions (as with the order of operations) we perform what is inside of the parentheses first. So, g(3)=2(3)+2=8 and then f(8)=24.
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The function 
is defined as 
. What is 
?
The function 
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Substitute -1 for 
in the given function.
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that 
is 1, then you will have calculated 18.
Substitute -1 for 
If you didn’t remember the negative sign, you will have calculated 36. If you remembered the negative sign at the very last step, you will have calculated -36; however, if you did not remember that 
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f(x) = 2x2 + x – 3 and g(y) = 2y – 7. What is f(g(4))?
f(x) = 2x2 + x – 3 and g(y) = 2y – 7. What is f(g(4))?
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To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).
g(4) = 2 x 4 – 7 = 1.
f(1) = 2 x 12 + 2 x 1 – 3 = 0.
To evaluate f(g(4)), one must first determine the value of g(4), then plug that into f(x).
g(4) = 2 x 4 – 7 = 1.
f(1) = 2 x 12 + 2 x 1 – 3 = 0.
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What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
What is the value of the function f(x) = 6x2 + 16x – 6 when x = –3?
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There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
There are two ways to do this problem. The first way just involves plugging in –3 for x and solving 6〖(–3)〗2 + 16(–3) – 6, which equals 54 – 48 – 6 = 0. The second way involves factoring the polynomial to (6x – 2)(x + 3) and then plugging in –3 for x. The second way quickly shows that the answer is 0 due to multiplying by (–3 + 3).
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For all positive integers, let k***** be defined by k*** =** (k-1)(k+2) . Which of the following is equal to 3***+4***?
For all positive integers, let k***** be defined by k*** =** (k-1)(k+2) . Which of the following is equal to 3***+4***?
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We can think of k❋ as the function f(k)=(k-1)(k+2), so 3❋+4❋is f(3)+f(4). When we plug 3 into the function, we find f(3)=(3-1)(3+2)=(2)(5)=10, and when we plug 4 into the function, we find f(4)=(4-1)(4+2)=(3)(6)=18, so f(3)+f(4)=10+18=28. The only answer choice that equals 28 is 5❋ which is f(5)=(5-1)(5+2)=(4)(7)=28.
We can think of k❋ as the function f(k)=(k-1)(k+2), so 3❋+4❋is f(3)+f(4). When we plug 3 into the function, we find f(3)=(3-1)(3+2)=(2)(5)=10, and when we plug 4 into the function, we find f(4)=(4-1)(4+2)=(3)(6)=18, so f(3)+f(4)=10+18=28. The only answer choice that equals 28 is 5❋ which is f(5)=(5-1)(5+2)=(4)(7)=28.
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Let the function f be defined by f(x)=x-t. If f(12)=4, what is the value of f(0.5*t)?
Let the function f be defined by f(x)=x-t. If f(12)=4, what is the value of f(0.5*t)?
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First we substitute in 12 for x and set the equation up as 12-t=4. We then get t=8, and substitute that for t and get f(0.5*8), giving us f(4). Plugging 4 in for x, and using t=8 that we found before, gives us:
f(4) = 4 - 8 = -4
First we substitute in 12 for x and set the equation up as 12-t=4. We then get t=8, and substitute that for t and get f(0.5*8), giving us f(4). Plugging 4 in for x, and using t=8 that we found before, gives us:
f(4) = 4 - 8 = -4
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If x must be an integer, which of the following could be the value of f(x)?
f(x) = 2x2 - 6
If x must be an integer, which of the following could be the value of f(x)?
f(x) = 2x2 - 6
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If f(x) = 2, then x will be 2. All other times x will yield a radical that cannot be reduced.
If f(x) = 2, then x will be 2. All other times x will yield a radical that cannot be reduced.
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When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer of x + 17.
When we multiply a function by a constant, we multiply each value in the function by that constant. Thus, 2f(x) = 4x + 12. We then subtract g(x) from that function, making sure to distribute the negative sign throughout the function. Subtracting g(x) from 4x + 12 gives us 4x + 12 - (3x - 3) = 4x + 12 - 3x + 3 = x + 15. We then add 2 to x + 15, giving us our answer of x + 17.
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The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
The cost of a cell phone plan is $40 for the first 100 minutes of calls, and then 5 cents for each minute after. If the variable x is equal to the number of minutes used for calls in a month on that cell phone plan, what is the equation f(x) for the cost, in dollars, of the cell phone plan for calls during that month?
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40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
40 dollars is the constant cost of the cell phone plan, regardless of minute usage for calls. We then add 5 cents, or 0.05 dollars, for every minute of calls over 100. Thus, we do not multiply 0.05 by x, but rather by (x - 100), since the 5 cent charge only applies to minutes used that are over the 100-minute barrier. For example, if you used 101 minutes for calls during the month, you would only pay the 5 cents for that 101st minute, making your cost for calls $40.05. Thus, the answer is 40 + 0.05(x - 100).
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f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
f(x) = 4x + 2
g(x) = 3x - 1
The two equations above define the functions f(x) = g(x). If f(d) = 2g(d) for some value of d, then what is the value of d?
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f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
f(x) = 4x + 2
g(x) = 3x - 1
We have f(d) = 2g(d). We multiply each value in g(d) by 2.
4d + 2 = 2(3d - 1) (Distribute the 2 in the parentheses by multiplying each value in them by 2.)
4d + 2 = 6d - 2 (Add 2 to both sides.)
4d + 4 = 6d (Subtract 4d from both sides.)
4 = 2d (Divide both sides by 2.)
2 = d
We can plug that back in to double check.
4(2) + 2 = 6(2) - 2
8 + 2 = 12 - 2
10 = 10
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The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
The function f, where f(x) = x2 + 6x + 8, is related to function g, where g(x) = 5 f(x-2). What is g(3)?
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Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
Doing things in an orderly way is a friend to the test-taker.
g(3) = 5 f(3-2)
= 5 f(1)
= 5 \[ 12 + 6**∙**1 + 8\]
= 5 \[ 1 + 6 + 8\]
= 5 \[ 15\]
= 75
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If 
and 
, what is 
?
If
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Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x2 – 12) + 7.
Distribute the 3: 3x2 – 36 + 7 = 3x2 – 29
Plug g(x) into f(x) as if it is just a variable. This gives f(g(x)) = 3(x2 – 12) + 7.
Distribute the 3: 3x2 – 36 + 7 = 3x2 – 29
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