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21 August, 03:36

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

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Answers (2)
  1. 21 August, 03:40
    0
    (k ∘ p) (x) = 2x^2-12x+13
  2. 21 August, 04:06
    0
    (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
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