Question

What is the inverse of the function f(x) = x – 12?

Answer 1

$\displaystyle g(x) = x + 12.$

Answer 2

Answer:  The required inverse of the given function is $f^{-1}(x)=x+12.$

Step-by-step explanation:  We are given to find the inverse of the following function :

$f(x)=x-12~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)$

Let us consider that

$f(x)=y~~~\Rightarrow x=f^{-1}y.$

So, from equation (i), we get

$f(x)=x-12\\\\\Rightarrow y=f^{-1}(y)-12\\\\ \Rightarrow f^{-1}(y)=y+12\\\\\Rightarrow f^{-1}(x)=x+12.$

Thus, the required inverse of the given function is $f^{-1}(x)=x+12.$