If $f$ is an even function, determine if $g$ is even, odd, or neither.
$$g ( x ) = f ( - x ) + 1$$
A) even
B) odd
C) cannot be determined
D) neither

Name: If $f$ is an even function, determine if $g$ is even, odd, or neither. \[g ( x ) = f ( - x ) + 1\] A) even B) odd C) cannot be determined D) neither
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Question

Quizplus · Accepted Answer

Since $f$ is an even function, $f(x) = f(-x)$. Therefore, $g(x) = f(-x) + 1 = f(x) + 1$, which means $g$ is also even because it satisfies the definition of an even function: $g(-x) = g(x)$.

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