Is the following function even, odd, or neither? f(x)=x^(4)+x Choose 1 answer: (A) Even (B) Odd (c) Neither

Symmetry properties of a function: To determine if the function f(x) is even, odd, or neither, we need to check the symmetry properties of the function. An even function satisfies f(x) = f(-x) for all x in its domain, while an odd function satisfies f(-x) = -f(x) for all x in its domain.Checking if f(x) is even: Let's first check if f(x) is even. We substitute -x for x in the function and see if we get the original function back. f(-x) = (-x)^(4) + (-x) = x^(4) - xChecking if f(x) is odd: We can see that f(-x) does not equal f(x), because f(x) = x^(4) + x and f(-x) = x^(4) - x. Therefore, the function f(x) is not even.Conclusion: Next, let's check if f(x) is odd. We substitute -x for x in the function and see if we get the negative of the original function. f(-x) = (-x)^(4) - x = x^(4) - xWe can see that f(-x) does not equal -f(x), because -f(x) would be -x^(4) - x, which is not equal to x^(4) - x. Therefore, the function f(x) is not odd.Since f(x) is neither even nor odd, the correct answer is that the function is neither even nor odd.

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Is the following function even, odd, or neither?

f(x)=x^(4)+x
Choose 1 answer:
(A) Even
(B) Odd
(c) Neither

Is the following function even, odd, or neither? $\newline$ $f(x)=x^{4}+x$ $\newline$ 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)=x^{4}+x

\newline

Choose

1

answer:

\newline

(A) Even

\newline

(B) Odd

\newline

Symmetry properties of a function: To determine if the function $f(x)$ is even, odd, or neither, we need to check the symmetry properties of the function. An even function satisfies $f(x) = f(-x)$ for all $x$ in its domain, while an odd function satisfies $f(-x) = -f(x)$ for all $x$ in its domain.
Checking if f(x) is even: Let's first check if f(x) is even. We substitute $-x$ for $x$ in the function and see if we get the original function back. $f(-x) = (-x)^{4} + (-x) = x^{4} - x$
Checking if $f(x)$ is odd: We can see that $f(-x) \neq f(x)$ , because $f(x) = x^{4} + x$ and $f(-x) = x^{4} - x$ . Therefore, the function $f(x)$ is not even.
Conclusion: Next, let's check if $f(x)$ is odd. We substitute $-x$ for $x$ in the function and see if we get the negative of the original function. $\newline$ $f(-x) = (-x)^{4} - x = x^{4} - x$
Conclusion: Next, let's check if $f(x)$ is odd. We substitute $-x$ for $x$ in the function and see if we get the negative of the original function. $\newline$ $f(-x) = (-x)^{4} - x = x^{4} - x$ We can see that $f(-x)$ does not equal $-f(x)$ , because $-f(x)$ would be $-x^{4} - x$ , which is not equal to $x^{4} - x$ . Therefore, the function $f(x)$ is not odd.
Conclusion: Next, let's check if $f(x)$ is odd. We substitute $-x$ for $x$ in the function and see if we get the negative of the original function. $f(-x) = (-x)^{4} - x = x^{4} - x$ We can see that $f(-x)$ does not equal $-f(x)$ , because $-f(x)$ would be $-x^{4} - x$ , which is not equal to $x^{4} - x$ . Therefore, the function $f(x)$ is not odd.Since $f(x)$ is neither even nor odd, the correct answer is that the function is neither even nor odd.