Question 1040340
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.