SOLUTION: https://ibb.co/VHjmjtW

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Question 1187566: https://ibb.co/VHjmjtW
Found 2 solutions by MathLover1, greenestamps:
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29=5x%2B4
inverse:
f%28x%29=y
y=5x%2B4...............swap variables
x=5y%2B4...........solve for y
x-4=5y
y=%28x-4%29%2F5
f%5E-1%28x%29=%28x-4%29%2F5
verify that f%28f%5E-1%28x%29%29=x and f%5E-1%28f%28x%29%29=x

f%28f%5E-1%28x%29%29=f%28%28x-4%29%2F5%29
=5%28%28x-4%29%2F5%29%2B4.....simplify
=x-4%2B4
=x

f%5E-1%28f%28x%29%29=f%5E-1%285x%2B4%29
=%285x%2B4-4%29%2F5+
=%285x%29%2F5+
=x

Answer by greenestamps(13334) About Me  (Show Source):
You can put this solution on YOUR website!


The solution from the other tutor shows a formal mathematical method for finding the inverse.

The problem says to find the inverse informally... although there is no way to know what that means.

One easy way to find the inverse of a relatively simple function is by using the concept that an inverse function "un-does" what the function does.

To undo what a function does, the inverse function must perform the opposite operations in the opposite order.

For a simple function like this one, finding the inverse function by this method is simple.

The given function performs the following operations on the input:
(1) multiple by 5; and
(2) add 4

The inverse function therefore needs to perform these operations on the input:
(1) subtract 4; and
(2) divide by 5

The inverse function is then

f%5E%28-1%29%28x%29=%28x-4%29%2F5