Question

Match the one-to-one functions with their inverse functions.
Inverse Function
f^-1(x)=4(20-x)<--->
f^-1(x)=x-7<---->
f^-1(x)=8(x+7)<---->
f^-1(x)=-3(x-1)<---->

Function
f(x)=x/8-7
f(x)=x+7
f(x)=1-x/3
f(x)=20-0.25x

Answer 1

The inverse of a function is obtained by making x the subject of the formular of the function.

Given the function
$f(x)= \frac{x}{8} -7$
the inverse of the function is obtained as follows:
$y= \frac{x}{8} -7 \\ \\ y+7=\frac{x}{8} \\ \\ x=8(y+7) \\ \\ \bold{f^{-1}(x)=8(x+7)}$

Given the function
[tex[f(x)=x+7[/tex]
the inverse of the function is obtained as follows:
$y=x+7 \\ \\ x=y-7 \\ \\ \bold{f^{-1}(x)=x-7}$

Given the function
$f(x)=1- \frac{x}{3}$
the inverse of the function is obtained as follows:
$y=1- \frac{x}{3} \\ \\ -\frac{x}{3} =y-1 \\ \\ x=-3(y-1) \\ \\ \bold{f^{-1}(x)=-3(x-1)}$

Given the function
$f(x)=20-0.25x$
the inverse of the function is obtained as follows:
$y=20-0.25x=20- \frac{1}{4} x \\ \\ \frac{1}{4} x=20-y \\ \\ x=4(20-y) \\ \\ \bold{f^{-1}(x)=4(20-x)}$