Evaluate the function \( h(x)=x^{4}-2 x^{2}+1 \) at the given values of the independent variable and simplify. \( \begin{array}{llll}\text { a. } h(3) & \text { b. } h(-1) & \text { c. } h(-x) & \text { d. } h(3 a)\end{array} \)

Let's evaluate the function \( h(x) = x^4 - 2x^2 + 1 \) at the given values of \( x \). **a.** To find \( h(3) \): \[ h(3) = (3)^4 - 2(3)^2 + 1 = 81 - 18 + 1 = 64. \] **b.** To find \( h(-1) \): \[ h(-1) = (-1)^4 - 2(-1)^2 + 1 = 1 - 2 + 1 = 0. \] **c.** To find \( h(-x) \): \[ h(-x) = (-x)^4 - 2(-x)^2 + 1 = x^4 - 2x^2 + 1 = h(x). \] This shows that the function is even. **d.** To find \( h(3a) \): \[ h(3a) = (3a)^4 - 2(3a)^2 + 1 = 81a^4 - 18a^2 + 1. \] So the results are: - **a.** \( h(3) = 64 \) - **b.** \( h(-1) = 0 \) - **c.** \( h(-x) = h(x) \) - **d.** \( h(3a) = 81a^4 - 18a^2 + 1 \)