Question

Given the functions k(x) = 2x2 − 7 and p(x) = x − 4, find (k ∘ p)(x).

Answer 1

For this case we have the following functions:

$k (x) = 2x ^ 2-7\\p (x) = x-4$

We must find$(k_ {0} p) (x)$. By definition of compound functions we have to:

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

So:

Taking into account that:

$(a-b) ^ 2 = a ^ 2-2ab + b ^ 2$

Different signs are subtracted and the major sign is placed.

$k (p (x)) = 2 (x-4) ^ 2-7 = 2 (x ^ 2-2 (x) (4) + 4 ^ 2) -7 = 2 (x ^ 2-8x + 16) -7 = 2x ^ 2-16x + 32-7 = 2x ^ 2-16x + 25$

Finally we have to:

$(k_ {o} p) (x) = 2x ^ 2-16x + 25$

Answer:

$(k_ {o} p) (x) = 2x ^ 2-16x + 25$