If f(x) = 3x and g(x) = 1/3x, which expression could be used to verify that g(x) is the inverse of f(x)?
3x(x/3), (1/3x)(3x), 1/3(3x), 1/3(1/3x)

Solution:

Given: Functions are f(x) = 3x and g(x) = 1/3x

(f∘g) and (g∘f) are the composite functions. (f∘g) takes all the inputs of the output of g(x) and (g∘f) takes all the inputs of f(x).

(f∘g) = f(g(x)) = f(1/3x) = 3(1/3x) = 1/x

(g∘f) = g(f(x)) = g(3x) = 1/ 3(3x) = 1/9x

Here (g∘f) can be written as 1/3(3x)

An inverse function is a function that "reverses" another function that is if the function f applied to an input x gives a result of y, then applying its inverse function g to y gives the result x.

Hence, by this expression 1/3(3x), we can say that f(x) is the inverse of g(x).

If f(x) = 3x and g(x) = 1/3x, which expression could be used to verify that g(x) is the inverse of f(x)?

Summary:

If f(x) = 3x and g(x) = 1/3x, 1/ 3(3x) expression could be used to verify that g(x) is the inverse of f(x).