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Example Questions
Example Question #171 : Functions
and
. Find
.
and
.
To find we plug in the function
everywhere there is a variable in the function
.
This is the composition of "f of g of x".
Foil the square and simplify:
Example Question #21 : Composition Of Functions
If and
, what must
be?
Evaluate the composite function first.
Solve for by substituting
into the
value for
.
The value of will be replaced inside
, which will become
.
Evaluate .
The value of is
. Add one to this value.
The answer is .
Example Question #21 : Composition Of Functions
Find given
and
To evaluate, first evaluate and then plug in that answer into
. Thus,
Then, is
Example Question #1131 : Pre Calculus
Find given the following.
To solve, plug 1 into g and then your answer into f.
Thus,
Plugging in this value into our f function we get the final answer as follows.
Example Question #1132 : Pre Calculus
Find given the following functions:
To solve, simply plug in 2 into f and then the result into g.
Thus,
Example Question #1133 : Pre Calculus
Suppose and
. Find
.
To find , you must subsititue
into the function,
.
Example Question #23 : Composition Of Functions
If and
, what is
First, we find or
Then, find
, or
Example Question #182 : Functions
Given and
find
.
None of these.
Finding is the same as plugging in
into
much like one would find
for a function
.
and
Insert g(x) into f(x) everywhere there is a variable in f(x):
Example Question #1139 : Pre Calculus
We are given the following:
and
.
Find:
None of the other answers.
None of the other answers.
Let's discuss what the problem is asking us to solve. The expression (read as as "f of g of x") is the same as
. In other words, we need to substitute
into
.
Substitute the equation of for the variable in the given
function:
Next we need to FOIL the squared term and simplify:
FOIL means that we multiply terms in the following order: first, outer, inner, and last.
First:
Outer:
Inner:
Last:
When we combine like terms, we get the following:
Substitute this back into the equation and continue to simplify.
None of the answers are correct.
Example Question #1131 : Pre Calculus
Simplify
.
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