If $f$ is an even function, determine if $g$ is even, odd, or neither.
$$g ( x ) = - f ( x + 3 )$$
A) even
B) odd
C) cannot be determined
D) neither

Question

Quizplus · Accepted Answer

Since $f$ is an even function, $f(x) = f(-x)$. However, without knowing the specific form of $f$, we cannot determine if $g(x) = -f(x+3)$ is even, odd, or neither. The transformation applied to $f$ does not allow us to conclude the parity of $g$ without additional information about $f$.

If fff Is an Even Function, Determine If ggg Is Even, Odd, or Neither

If $f$ Is an Even Function, Determine If $g$ Is Even, Odd, or Neither