Question

Suppose f(x)= 5-x/3 (tion) and g(x) = 5-3x. Use composition of functions to show f(x) and g(x) are inverses of each other.Write a conclusion statement to complete your proof. solve step by step show work

Answer 1

f(g(x)) = x and g(f(x)) = x for all x in their respective domains, proving that f(x) and g(x) are inverses of each other.

Step-by-step explanation:

To show that f(x) and g(x) are inverses of each other, we need to prove two things:

1. f(g(x)) = x for all x in the domain of g(x)
2. g(f(x)) = x for all x in the domain of f(x)

Let's start by finding the composition of f(g(x)):

f(g(x)) = f(5-3x) = 5 - (5-3x)/3 = 5 - (5/3) + x = x

Now let's find the composition of g(f(x)):

g(f(x)) = g(5-x/3) = 5 - 3(5-x/3) = 5 - (15 - x) = x

Since we have shown both f(g(x)) = x and g(f(x)) = x for all x in their respective domains, we can conclude that f(x) and g(x) are inverses of each other.