Question

What's the difference between f(x)^2 and f(x^2)

Answer 1

Consider the function f(x) = x + 1. Then
\[ f(x^2) = x^2 + 1 \]
but
\[ f(x)^2 = (x+1)^2 = x^2 + 2x + 1 \]
Hence they are not equal in general.

Answer 2

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