Question

The Martians ask you to explain one last thing, Ultimate Math Ambassador. Assign any number to x. Using complete sentences, explain whether f(g(x)) and g(f(x)) will always result in the same number. You will use the inverse function that you created in problem number 5 for g(x).

Answer 1

Both f(g(x)) and g(f(x)) will always result in whatever number you assign to x. For example, if you assign 12 to x. f(g(x)) will equal 12, as will g(f(x)).

Answer 2

In general, if g(x) is the inverse of f(x), f(g(x)) = g(f(x)) = x

Answer 3

Ok, that makes sense. Now, how do I work g(x) = (x - 3)/5?

Answer 4

@BangkokGarrett

Answer 5

P.S. my inverse function is g(x) = (x - 3)/5.