Problem 22 - College Algebra Essentials

Question

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

Step-by-Step Solution

Answer

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

Step 1: Write down the initial function

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

Step 2: Substitute every \(x\) with \(-x\)

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

Step 3: 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.