Determine algebraically whether the function is even, odd, or neither.
-$$f ( x ) = \sqrt { x }$$
A) even
B) odd
C) neither

Question

Quizplus · Accepted Answer

The function $f(x) = \sqrt{x}$ is neither even nor odd because it does not satisfy the conditions for either. For a function to be even, $f(x) = f(-x)$ must hold, which is not true for $\sqrt{x}$ since $\sqrt{-x}$ is not defined for real numbers when $x > 0$. For a function to be odd, $f(-x) = -f(x)$ must hold, which is also not true for $\sqrt{x}$ since there is no way to manipulate $\sqrt{x}$ to equal $-\sqrt{x}$.

Determine Algebraically Whether the Function Is Even, Odd, or Neither f(x)=xf ( x ) = \sqrt { x }f(x)=x​

Determine Algebraically Whether the Function Is Even, Odd, or Neither $f ( x ) = \sqrt { x }$