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, it satisfies the property $f(-x) = f(x)$. However, without specific information about the form of $f(x)$, we cannot conclusively determine if $g(x) = -f(x + 3)$ is even, odd, or neither. The transformation applied to $f$ could potentially alter its symmetry properties, but without knowing the specifics of $f$, we cannot make a definitive determination about $g$.

If F Is an Even Function, Determine If G Is g(x)=−f(x+3)g ( x ) = - f ( x + 3 )g(x)=−f(x+3)

If F Is an Even Function, Determine If G Is $g ( x ) = - f ( x + 3 )$