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Chapter 2: Problem 22

Determine whether each function is even, odd, or neither. $$h(x)=2 x^{2}+x^{4}$$

Short Answer

Expert verified
The function \(h(x) = 2x^2 + x^4\) is an even function.

Step by step solution

01

Write down the initial function

The function that needs to be analyzed is given by \(h(x) = 2x^2 + x^4\).
02

Substitute every \(x\) with \(-x\)

By substituting each \(x\) with \(-x\) we get \(h(-x) = 2(-x)^2 + (-x)^4\). This simplifies to \(h(-x) = 2x^2 + x^4\).
03

Compare \(h(x)\) and \(h(-x)\)

After simplifying \(h(-x)\), it can be seen that it equals to the original function \(h(x)\). Therefore, \(h(x) = h(-x)\). This indicates that the function \(h(x)\) is even.

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Most popular questions from this chapter

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