We can see this by seeing
\[ T(f+g)(x) = ( f(x) + g(x) )^2 = f^2(x) + 2 f(x) g(x) + g^2 (x) \]
while
\[ T(f)(x) + T(g)(x) = f^2(x) + g^2(x) . \]
Because $T(f+g) \neq T(f) + T(g)$, we see that $T$ is not a linear transformation.

For a specific example, consider $f(x) = g(x) = x$. Then
\[ T( f+g)(x) = (2x)^2 = 4x^2 , \]
while
\[ T(f)(x) + T(g)(x) = x^2 + x^2 = 2x^2 . \]
Clearly $T(f+g) \neq T(f) + T(g)$.

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