For this case we have the following functions:
[tex]k (x) = 2x ^ 2-7\\p (x) = x-4[/tex]
We must find[tex](k_ {0} p) (x)[/tex]. By definition of compound functions we have to:
[tex](k_ {0} p) (x) = k (p (x))[/tex]
So:
Taking into account that:
[tex](a-b) ^ 2 = a ^ 2-2ab + b ^ 2[/tex]
Different signs are subtracted and the major sign is placed.
[tex]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[/tex]
Finally we have to:
[tex](k_ {o} p) (x) = 2x ^ 2-16x + 25[/tex]
Answer:
[tex](k_ {o} p) (x) = 2x ^ 2-16x + 25[/tex]
