Answer :
Answer:
[tex]\implies f^{-1}(x) =-\dfrac{x}{4}-3 [/tex]
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 :-
[tex]\implies f(x) = -4x - 12 \\\\\implies y = -4x-12 [/tex]
Interchanging x and y :-
[tex]\implies x = -4y - 12 [/tex]
Solve out for y :-
[tex]\implies x = -4y - 12 \\\\\implies -4y = x +12 \\\\\implies y =\dfrac{x+12}{-4}\\\\\implies y =-\dfrac{x}{4}-3 [/tex]
Replace y with f-¹(x) :-
[tex]\implies f^{-1}(x) =-\dfrac{x}{4}-3 [/tex]
Hence the inverse of the function is -x/4-3 .