Question

For the functions f(x) = 6x – 1 and g(x) = 4x2 + x, find (gºf)(x). Provide your answer bolow

Answer 1

For this case we have the following functions:

$f (x) = 6x-1\\g (x) = 4x ^ 2 + x$

We must find $(g_ {o} f) (x):$

By definition of composition of functions we have to:

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

So:

$(g_ {o} f) (x) = 4 (6x-1) ^ 2 + (6x-1) = 4 ((6x) ^ 2-2 (6x) (1) + (1) ^ 2) + 6x -1 = 4 (36x ^ 2-12x + 1) + 6x-1 = 144x ^ 2-48x + 4 + 6x-1 = 144x ^ 2-42x + 3$

We have different signs subtracted and the sign of the major is placed.

Finally we have to:

$(g_ {o} f) (x) = 144x ^ 2-42x + 3$

ANswer:

$(g_ {o} f) (x) = 144x ^ 2-42x + 3$