Questions: Evaluate the function h(x) = x^4 + 5x^2 + 3 at the given values of the independent variable and simplify. a. h(3) b. h(-1) c. h(-x) d. h(3a) a. h(3) = (Simplify your answer.) b. h(-1) = (Simplify your answer.) c. h(-x) = (Simplify your answer.) d. h(3a) = (Simplify your answer.)

Evaluate the function h(x) = x^4 + 5x^2 + 3 at the given values of the independent variable and simplify.
a. h(3)
b. h(-1)
c. h(-x)
d. h(3a)
a. h(3) = (Simplify your answer.)
b. h(-1) = (Simplify your answer.)
c. h(-x) = (Simplify your answer.)
d. h(3a) = (Simplify your answer.)

Transcript text: Evaluate the function $h(x)=x^{4}+5 x^{2}+3$ at the given values of the independent variable and simplify. a. $\mathrm{h}(3)$ b. $h(-1)$ c. $\mathrm{h}(-\mathrm{x})$ d. $\mathrm{h}(3 \mathrm{a})$ a. $h(3)=$ $\square$ (Simplify your answer.) b. $h(-1)=$ $\square$ (Simplify your answer.) c. $h(-x)=$ $\square$ (Simplify your answer.) d. $h(3 a)=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

To evaluate the function $ h(x) = x^4 + 5x^2 + 3 $ at the given values, we will substitute the specified values into the function and simplify the resulting expressions.

a. For $ h(3) $, substitute $ x = 3 $ into the function. b. For $ h(-1) $, substitute $ x = -1 $ into the function. c. For $ h(-x) $, substitute $ x = -x $ into the function.

Step 1: Evaluate $ h(3) $

To evaluate $ h(3) $, we substitute $ x = 3 $ into the function: \[ h(3) = 3^4 + 5 \cdot 3^2 + 3 = 81 + 45 + 3 = 129 \]

Step 2: Evaluate $ h(-1) $

Next, we evaluate $ h(-1) $ by substituting $ x = -1 $: \[ h(-1) = (-1)^4 + 5 \cdot (-1)^2 + 3 = 1 + 5 + 3 = 9 \]

Step 3: Evaluate $ h(-x) $

For $ h(-x) $, we substitute $ x = -x $ into the function: \[ h(-x) = (-x)^4 + 5 \cdot (-x)^2 + 3 = x^4 + 5x^2 + 3 \]