Question

Find the inverse of f(x) = -4x - 12​

Answer 1

Answer:

$\implies f^{-1}(x) =-\dfrac{x}{4}-3$

Step-by-step explanation:

Given :-

• f(x) = -4x-12

And we need to find out the Inverse of the function . Let us assume that f(x) = y . Now , firstly replace x with y and vice versa.

Function :-

$\implies f(x) = -4x - 12 \\\\\implies y = -4x-12$

Interchanging x and y :-

$\implies x = -4y - 12$

Solve out for y :-

$\implies x = -4y - 12 \\\\\implies -4y = x +12 \\\\\implies y =\dfrac{x+12}{-4}\\\\\implies y =-\dfrac{x}{4}-3$

Replace y with f-¹(x) :-

$\implies f^{-1}(x) =-\dfrac{x}{4}-3$

Hence the inverse of the function is -x/4-3 .