Question

For the given functions f and g, find the indicated composition. f(x) = 4x2 + 6x + 5; g(x) = 6x - 7 (gof)(x) (gof)(x) =___

Answer 1

`\huge{ \boxed{(g \: o \: f)(x) = 24 {x}^(2) + 36x + 23}}`

Explanation:

`f(x) = 4 {x}^(2) + 6x + 5 \\ g(x) = 6x - 7 \: \: \: \: \: \: \: \: \: \: \: \: \:`

To find (gof)(x), substitute f(x) into g(x). That is for every x in g (x) replace it with f(x) and solve.

`(g \: o \: f)(x) = 6(4 {x}^(2) + 6x + 5) - 7 \\ \implies24 {x}^(2) + 36x + 30 - 7 \\ = {24x}^(2) + 36x + 23`