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Example Questions
Example Question #1 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we switch the switch the and
variables in the function.
Switching and
gives
Then, solving for gives our answer:
Example Question #11 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we must swtich and
variables in the function.
Switching and
gives:
Solving for yields our final answer:
Example Question #12 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we can switch and
in the function and solve for
:
Switching and
gives:
Solving for yields our final answer:
Example Question #11 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we can switch and
in the function and solve for
.
Switch and
:
We can now solve for :
Example Question #11 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we simply need to switch the values of and
and solve for
.
Switching and
, we can write the function as:
We now subtract to solve for :
Example Question #12 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of this function, we switch and
in the function:
We now solve for :
Example Question #13 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of this function we can switch the and
variables and solve for
.
First, switch and
in the function:
Now, solve for :
Example Question #101 : Functions
Find the inverse of .
To find the inverse of the function, we switch and
in the function.
We can now find our answer by solving for :
Example Question #15 : Find The Inverse Of A Function
Find the inverse of .
To find the inverse of the function, we swtich and
in the function.
Solve for :
Example Question #16 : Find The Inverse Of A Function
Find the inverse of this function:
In order to have the inverse of a function, the new function must perform the inverse opperations in the opposite order. One way to ensure that is true is to consider the case of , switch x and y, then solve for y.
in this case becomes
.
Our first step in solving is to take the reciprocal power on each side.
The reciprocal of 5 is , so we'll take both sides to the power of 0.2:
Now divide by 2:
Note that the answer has the correct inverse opperations, it is just in the wrong order - first you divide by 2, then you take x to the power of 0.2.
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