Question

April was asked to determine whether f(x)=x^3 -1 is even, odd, or neither. Here is her work:

Answer 1

April's work in checking for the function, $f(x) = x^3 - 1$, to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took $f(-x) = - f(x)$, which was not true, since $f(-x) = -x^3 - 1$, whereas $- f(x) = -x^3 + 1$.

A function f(x) is said to be odd or even when it completes the condition:

• f(-x) = -f(x), for f(x) to be an odd function, and
• f(-x) = f(x), for f(x) to be an even function.

In the question, we are given that April was asked to determine whether  $f(x) = x^3 - 1$, is even, odd, or neither, and are shown her work.

We are asked whether April's work is correct, and if not, what is the first step where April made a mistake.

To check for a function is even or odd, we first calculate f(-x).

April's first step was also finding f(-x), which she found accurately as  $f(-x) = -x^3 - 1$.

Next, we need to check whether f(-x) is equal to f(x), -f(x), or neither, to check if the function is even, odd, or neither, respectively.

April, also choose the right step of checking, but did a mistake in checking, since f(-x) ≠ f(x), and also, f(-x) ≠ - f(x), since, $- f(x) = -(x^3 - 1)$ = $-x^3 + 1$, which is not equal to f(-x).

Thus, April's work in checking for the function, $f(x) = x^3 - 1$, to be even, odd, or neither, is incorrect. She did a mistake in step 2, where she took f(-x) = - f(x), which was not true, since $f(-x) = -x^3 - 1$, whereas $- f(x) = -x^3 + 1$.

Learn more about odd and even functions at

brainly.com/question/12207506

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