Question

Find the inverse of f(x) = -4x - 12​

Answer 1

`\implies f^(-1)(x) =-(x)/(4)-3`

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 =(x+12)/(-4)\\\\\implies y =-(x)/(4)-3`

Replace y with f-¹(x) :-

`\implies f^(-1)(x) =-(x)/(4)-3`

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