Given the functions k(x) = 2x^2 − 5 and p(x) = x − 3, find (k ∘ p)(x).
a. (k ∘ p)(x) = 2x^2 − 6x + 4
b. (k ∘ p)(x) = 2x^2 − 12x + 13
c. (k ∘ p)(x) = 2x^2 − 12x + 18
d. (k ∘ p)(x) = 2x2 − 8

The composite function is

Option b is correct.

Given function are,

We have to find composite function .

Thus, the composite function is

Learn more about the composite function here:

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(k ∘ p)(x)=2x^2-12x+13

Step-by-step explanation:

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

Use foil on (x-3)(x-3) or use this as a formula:

(x+a)^2=x^2+2ax+a^2.

(k ∘ p)(x)=k(p(x))

(k ∘ p)(x)=k(x-3)

(k ∘ p)(x)=2(x-3)^2-5

(k ∘ p)(x)=2(x-3)(x-3)-5

(k ∘ p)(x)=2(x^2-6x+9)-5

Distribute: multiply terms inside ( ) by 2:

(k ∘ p)(x)=2x^2-12x+18-5

(k ∘ p)(x)=2x^2-12x+13