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Question

# Determine whether the following statements are true and give an explanation or counterexample. In general, f(g(x))=g(f(x)).

Solution

Verified
Step 1
1 of 2

Counterexample:

$f(x)=x+1$

$g(x)=x^2$

$f(g(x))=f(x^2)=x^2+1$

$g(f(x))=g(x+1)=(x+1)^2=x^2+2x+1$

Statement is false.

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