I am too embarassed to ask this Calculus (really pre-calculus) question in tutoring, because I know I should know. Is the inverse of f(x)=3x-1 actually f(x)=1/3x+1? How do I find it? What if it asks the same equation replaced with f to the -1 power (x)? I think I know how the F of -1 power (x) is x+1/3, but I know that from watching someone else.

Answer 1

Ok. An inverse function is formed from switch in the input and output variables(x,y).

so y = 3x -1
flip x = 3y-1 and solve for y again
x+1=3y
y = 1/3(x+1)
so f^-1(x) = 1/3(x+1)
and the inverse of an inverse function is the original equation: f(x) = 3x-1

Answer 2

okay, thanks!