Question

1) f(x) = 2x + 4, g(x) = 4x2 + 1; Find (g ∘ f)(0).

Answer 1

`(g \: \circ \: f)(0) = 17`

Explanation:

f(x) = 2x + 4

g(x) = 4x² + 1

In order to find (g ∘ f)(0) we must first find

(g ° f )(x)

To find (g ° f )(x) substitute f(x) into g(x) that's for every x in g(x) replace it with f(x)

That's

`(g \: \circ \: f)(x) = 4( ({2x + 4})^(2) ) + 1 \\ = 4(4 {x}^(2) + 16x + 16) + 1 \\ = {16x}^(2) + 64x + 16 + 1`

We have

`(g \: \circ \: f)(x) = {16x}^(2) + 64x + 17 \\`

Now to find (g ∘ f)(0) substitute the value of x that's 0 into (g ∘ f)(0)

We have

`(g \: \circ \: f)(0) = 16( {0})^(2) + 64(0) + 17 \\`

We have the final answer as

`(g \: \circ \: f)(0) = 17`

Hope this helps you