How do you verify that f(x)=3x+5; g(x)=1/3x-5/3 are inverses?

1 Answer
Feb 22, 2017

If (f @ g)(x) = x and (g @ f)(x) = x then f(x) and g(x) are inverse functions

Explanation:

There are three ways to verify that these functions are inverse functions:

  1. (f @ g)(x) = f(g(x)) = 3(1/3x-5/3)+5 = x-5+5 = x (g @ f)(x) = g(f(x)) = 1/3(3x+5)-5/3 = x + 5/3 - 5/3 = x Therefore f(x) and g(x) are inverse functions.

  2. Let f(x) = y. Interchange x with y, then solve for y. You should get g(x): x = 3y+5, x-5=3y, y=1/3x - 5/3 = g(x)

  3. Graph both functions and the y=x line. The functions should be reflections of each other across the y=x line. This means for each point (a,b) from f(x) there should be a (b,a) point on g(x).