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

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

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Check Symmetry Properties: 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, and an odd function satisfies f(-x) = -f(x) for all x in its domain.Check if f(x) is Even: First, we will check if f(x) is even. We calculate f(-x) and see if it is equal to f(x). f(-x) = ((-x)^3)/((-x)+1) = (-x^3)/(-x+1) = -x^3/(1-x)Compare f(-x) with f(x): Now we compare f(-x) with f(x). f(x) = x^3/(x+1) f(-x) = -x^3/(1-x) We can see that f(-x) is not equal to f(x), because f(x) has x+1 in the denominator, while f(-x) has 1-x (which is -(x+1)). Therefore, f(x) is not even.Check if f(x) is Odd: Next, we will check if f(x) is odd. We calculate f(-x) and see if it is equal to -f(x). We already have f(-x) = -x^3/(1-x) Now we calculate -f(x) = -(x^3/(x+1)) = -x^3/(x+1)Compare f(-x) with -f(x): We compare f(-x) with -f(x). f(-x) = -x^3/(1-x) -f(x) = -x^3/(x+1) We can see that f(-x) is not equal to -f(x), because the denominators are different: (1-x) is not the same as (x+1). Therefore, f(x) is not odd.Conclusion: Since f(x) is neither even nor odd, the correct answer is (C) Neither.

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

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