What is the inverse of the function f(x) = x/4 - 12?

Solution:

Given f(x) = x/4 - 12

Let y = f(x) = x/4 - 12

Let us swap the variables x,y and then solve for y, to get the inverse of f(x)

⇒ x = y/4 -12 = f(y)

⇒ x = (y - 48) /4

⇒ 4x = y - 48

⇒ 4x + 48 = y

⇒ 4(x + 12) = y

Since, x = f(y); f^-1(x) = y

Therefore, inverse f^-1(x) = y = 4(x + 12)

What is the inverse of the function f(x) = x/4 - 12?

Summary:

The inverse of the function f(x) = 1/4x - 12 is f^-1(x) = 4(x + 12).