Need help with quadratic functions.

Question

what is the function f(x) if f^-1(x)=x/8+3 ?

Answer 1

also, to check your work, take the compositions of the two functions and you should get "x" for an answer each time

f(x)=8x-24

f^-1(x)=(x/8)+3

f(f^-1x)=f([x/8]+3)=8([x/8]+3)-24=x+24-24=x

f^-1(f[x])=f^-1(8x-24)=[(8x-24)/8]+3=x-3+3=x

Answer 2

In order to solve for the inverse of a function, you must switch the x and y variables and then solve for y. In this example, you would substitute f^-1(x) for y, so that you have y=x/8+3. Then you would swap the variables to obtain x=y/8+3. Then to solve for y, you subtract 3 from each side to yield x-3=y/8. Then to isolate y, you multiply each side of the equation by 8. This results in an answer of y=8x-24.