Define f(x)=3x-8. If f^-1 is the inverse of f, find the value (s) of x for which f(x)=f^-1(x). Thank you!
f^-1(x) = (x+8)/3
So, we want
(x+8)/3 = 3x-8
x+8 = 9x-24
8x = 32
x = 4
3*4-8 = 4
(4+8)/3 = 4
Note that the same results could have been achieved by setting
f(x) = x
3x-8 = x
2x = 8
x = 4
Why? because f(f^-1) = x by definition.
So, if f^-1(x) = f(x), then
f^-1(f) = f^-1(x)
x = f^-1(x) = f(x)