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Chapter 2: Problem 63

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

Calculation of \(g(-x)\)

The function \(g(x)\) is given by \(x^{2}+x\). To find \(g(-x)\), substitute \(-x\) in place of \(x\) in the function: \(g(-x) = (-x)^{2} + (-x) = x^{2} - x\).
02

Compare \(g(-x)\) with \(g(x)\) and \(-g(x)\)

The function \(g(x)\) is \(x^{2}+x\), and \(g(-x)\) has been found to be \(x^{2} - x\). So, it is clear that \(g(-x) \neq g(x)\) since \(x^{2}+x \neq x^{2} - x\). So, the function \(g(x)\) is not even. Now, let's determine if the function is odd by comparing \(g(-x)\) with \(-g(x)\). The negative of function \(g(x)\) is \(-g(x) = -x^{2} - x\), which is also different from \(g(-x)\), as \(-x^{2} - x \neq x^{2} - x\). Therefore, the function \(g(x)\) is neither even nor odd.

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Most popular questions from this chapter

You will be developing functions that model given conditions. A car was purchased for \(\$ 22,500 .\) The value of the car decreases by \(\$ 3200\) per year for the first six years. Write a function that describes the value of the car, \(V\), after \(x\) years, where \(0 \leq x \leq 7 .\) Then find and interpret \(V(3)\)

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