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Chapter 2: Problem 20

Determine whether each function is even, odd, or neither. $$g(x)=x^{2}-x$$

Short Answer

Expert verified
The function \(g(x)=x^{2}-x\) is neither even nor odd.

Step by step solution

01

Analyze the function

First, consider the function \(g(x)=x^{2}-x\). This is a polynomial function of degree 2.
02

Test for evenness

To check if it is an even function, we replace \(x\) by \(-x\) in the function and simplify. This gives \(g(-x)=(-x)^{2}-(-x)=x^{2}+x\). Comparing this with the original function \(g(x)=x^{2}-x\), it's clear that \(g(x) 鈮� g(-x)\), therefore, the function is not even.
03

Test for oddness

To check if it is an odd function, we need to compare \(g(x)\) and \(-g(-x)\). We already have \(g(-x)\) from Step 2, so \(-g(-x)=-(x^{2}+x)=-x^{2}-x\). Comparing this to the original function \(g(x)=x^{2}-x\), it can be seen that \(g(x) 鈮� -g(-x)\), therefore the function is not odd.

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