what is the equation for f ^-1(x)

Question

if f(x)=(1/2)x-6 , what is the equation for f ^-1(x)

Answer 1

The function is f(x)  =  (1/2)x - 6

Find the inverse of the function.

Change y  =   (1/2)x - 6

Interchange x and y.

x  =   (1/2)y - 6

Solve for y.

x  =   (1/2)y - 6

x + 6  =   y/2

y  =  2(x + 6)

​y  =  2x + 12

Change y to f^-1 (x).

f^-1 (x)  =  2x + 12

Answer :

f^-1 (x)  =  2x + 12