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

(k ∘ p) (x) = 2x^2-12x+13

(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