Determine whether the function below is even, odd, or neither. $f ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec x$
A)Even
B)Odd
C)Neither

Question

Determine whether the function below is even, odd, or neither.  $f ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec x$  
A)Even
B)Odd
C)Neither

Quizplus · Accepted Answer

The function $f(x) = \frac{x^2}{3} - 3\sec x$ is even because both terms exhibit even symmetry. The term $\frac{x^2}{3}$ is even since $f(-x) = \frac{(-x)^2}{3} = \frac{x^2}{3}$, and the term $-3\sec x$ is even because $\sec(-x) = \sec x$. Therefore, the function is even as it satisfies $f(-x) = f(x)$ for all $x$ in its domain.

Determine Whether the Function Below Is Even, Odd, or Neither f(x)=x23−3sec⁡xf ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec xf(x)=3x2​−3secx

Determine Whether the Function Below Is Even, Odd, or Neither $f ( x ) = \frac { x ^ { 2 } } { 3 } - 3 \sec x$