Question

Evaluate the function
`h(x) = x^4 - 3 x^2 + 3` at the given values of the independent variable and simplify.

a. h(-3)
b. h(-1)
c. h(-x)
d. h(3a)

Answer 1

a. 57

b. 1

c.
`h(-x) = x^4 -3x^2 + 3`

d.
`h(3a) = 81a^4 -27a^2 + 3`

Explanation:

The independent variable in the function is
`x`.

a. When
`x = -3`:

`h(-3) = (-3)^4 - 3(-3)^2 +3\\\\\\h(-3) = 81 -3(9) + 3\\\\\\h(-3) = 81-27+3\\\\\\h(-3) = 57`

b. When
`x = -1:`

`h(-1) = (-1)^4 - 3(-1)^2 + 3\\\\\\h(-1) = 1 -3 + 3\\\\\\h(-1) = 1`

c. When
`x = -x`:

`h(-x) = (-x)^4 - 3(-x)^2 + 3\\\\\\\h(-x) = x^4 -3x^2 + 3`

d. When
`x = 3a`:

`h(3a) = (3a)^4 - 3(3a)^2 + 3\\\\\\h(3a) = 81a^4 - 3(9a^2) + 3\\\\\\h(3a) = 81a^4 -27a^2 + 3`