# Question #9e045

##### 1 Answer

#### Explanation:

The trick here is to realize that for a given value, the **inverse function** has its *output* as the *input* of the original function *for the same value*.

This means that if you plug something into the original function (the red apples), you will get an output (the yellow pears). If you then plug that output (the yellow pears) into the inverse function, you will get the *something* (the red apples) that you plugged into the original function.

The problem wants you to determine the output of the **inverse function** of *inverse function* is equal to

#f^(-1)(color(blue)(27)) = ?#

In other words, you need to find the *input* of *output* is equal to

So you need

#f(?) = 3 * ? = color(blue)(27)#

This will give you

#? = color(blue)(27)/3 = color(red)(9)#

Therefore,

So, if you plug **inverse function**, you will get

#f(color(red)(9)) = 3 * color(red)(9) = color(blue)(27)#

#f^(-1)(color(blue)(27)) = color(blue)(27)/3 = color(red)(9)#

This shows that the inverse function takes the form

#f^(-1)(x) = x/3#