Is the following function even, odd, or neither? f(x)=root(3)(x)-x Choose 1 answer: (A) Even (B) Odd (c) Neither

Determining Function Symmetry: To determine if the function f(x) = ∛x - x is even, odd, or neither, we need to check the symmetry properties of the function. A function is even if f(-x) = f(x) for all x in the domain, and it is odd if f(-x) = -f(x) for all x in the domain.Checking for Even Symmetry: First, let's check if the function is even. We calculate f(-x) and see if it is equal to f(x). f(-x) = ∛(-x) - (-x) = -∛x + x Now we compare this to f(x): f(x) = ∛x - x Clearly, f(-x) is not equal to f(x), so the function is not even.Checking for Odd Symmetry: Next, let's check if the function is odd. We calculate f(-x) and see if it is equal to -f(x). We already have f(-x) from the previous step: f(-x) = -∛x + x Now we calculate -f(x): -f(x) = -1 * (∛x - x) = -∛x + x We see that f(-x) is equal to -f(x), so the function is odd.

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Is the following function even, odd, or neither?

f(x)=root(3)(x)-x
Choose 1 answer:
(A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=\sqrt[3]{x}-x$ $\newline$ Choose $1$ answer: $\newline$ (A) Even $\newline$ (B) Odd $\newline$ (C) Neither

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Math Problems

Algebra 2

Symmetry and periodicity of trigonometric functions

Full solution

Q. Is the following function even, odd, or neither?

\newline

f(x)=\sqrt[3]{x}-x

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Determining Function Symmetry: To determine if the function $f(x) = \sqrt[3]{x} - x$ is even, odd, or neither, we need to check the symmetry properties of the function. A function is even if $f(-x) = f(x)$ for all $x$ in the domain, and it is odd if $f(-x) = -f(x)$ for all $x$ in the domain.
Checking for Even Symmetry: First, let's check if the function is even. We calculate $f(-x)$ and see if it is equal to $f(x)$ . $\newline$ $f(-x) = \sqrt[3]{-x} - (-x) = -\sqrt[3]{x} + x$ $\newline$ Now we compare this to $f(x)$ : $\newline$ $f(x) = \sqrt[3]{x} - x$ $\newline$ Clearly, $f(-x)$ is not equal to $f(x)$ , so the function is not even.
Checking for Odd Symmetry: Next, let's check if the function is odd. We calculate $f(-x)$ and see if it is equal to $-f(x)$ . $\newline$ We already have $f(-x)$ from the previous step: $\newline$ $f(-x) = -\sqrt[3]{x} + x$ $\newline$ Now we calculate $-f(x)$ : $\newline$ $-f(x) = -1 \times (\sqrt[3]{x} - x) = -\sqrt[3]{x} + x$ $\newline$ We see that $f(-x)$ is equal to $-f(x)$ , so the function is odd.