SOLUTION: Can I please have your assistance? If f(x) = 1 and g(x) = x2, what is f o g? What is g o f?

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Question 1040340: Can I please have your assistance? If f(x) = 1 and g(x) = x2, what is f o g? What is g o f?
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Given functions:
f(x) = 1
g(x) = x^2

Note: Type x^2 to mean "x squared"

"f o g" or (f o g)(x) is the same as f(g(x))

We start with f(x) = 1. We simply replace EVERY copy of x with g(x) to get f(g(x)) = 1

So we go from f(x) = 1 to f(g(x)) = 1

There are no 'x's on the right side. So there's nothing to replace on the right side.

Because f(g(x)) = 1, this means (f o g)(x) = 1 for all real numbers x. Whatever you plug in for x, the result is going to be 1.

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(g o f)(x) is the same as g(f(x))

g(x) = x^2 .... start with the given function for g(x)

g(f(x)) = [f(x)]^2 ... replace every copy of 'x' with f(x)

g(f(x)) = [1]^2 ... replace f(x) with 1. This is because f(x) = 1

g(f(x)) = 1 ... simplify

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So both (f o g)(x) and (g o f)(x) are equal to 1.