Question

Given ƒ(x) = 7x + 1 and g(x) = x^2, find (g ○ ƒ)(x)

Answer 1

For this case we have the following functions:

$f (x) = 7x + 1\\g (x) = x ^ 2$

We must find$(g_ {0} f) (x).$

By definition of composition of functions we have to:

$(g_ {0} f) (x) = g (f (x))$

So:

$(g_ {0} f) (x) = g (f (x)) = (7x + 1) ^ 2 = 49x ^ 2 + 2 (7x) (1) + 1 = 49x ^ 2 + 14x + 1$

ANswer:

$(7x + 1) ^ 2 = 49x ^ 2 + 14x + 1$