Question

Given the functions k(x) = 2x2 − 8 and p(x) = x − 4, find (k ∘ p)(x).

(k ∘ p)(x) = 2x2 − 16x + 24
(k ∘ p)(x) = 2x2 − 8x + 8
(k ∘ p)(x) = 2x2 − 16x + 32
(k ∘ p)(x) = 2x2 − 12

Answer 1

The answer is A. (k o p) (x)=2x^2-16x+24

Explanation:

Answer 2

`(k_ {0} p) (x) = 2x^2 -16x + 24`

Solution:

Given functions are:

`k(x) = 2x^2 - 8\\\\p(x) = x-4`

To Find:
`(k_ {0} p) (x)`

By definition of compound functions,

`(k_ {0} p) (x) = k (p (x))`

Substitute p(x) value in x place in k(x)

`(k_ {0} p) (x) = 2(x-4)^2-8\\\\Expand\\\\(k_ {0} p) (x) =2(x^2 -8x +16) - 8\\\\(k_ {0} p) (x) = 2x^2 -16x + 32-8\\\\Simplify\\\\(k_ {0} p) (x) = 2x^2 -16x + 24`

Thus the required is found