Answer:
[tex](g \: \circ \: f)(0) = 17[/tex]
Step-by-step 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
[tex](g \: \circ \: f)(x) = 4( ({2x + 4})^{2} ) + 1 \\ = 4(4 {x}^{2} + 16x + 16) + 1 \\ = {16x}^{2} + 64x + 16 + 1[/tex]
We have
[tex](g \: \circ \: f)(x) = {16x}^{2} + 64x + 17 \\ [/tex]
Now to find (g ∘ f)(0) substitute the value of x that's 0 into (g ∘ f)(0)
We have
[tex](g \: \circ \: f)(0) = 16( {0})^{2} + 64(0) + 17 \\ [/tex]
We have the final answer as
[tex](g \: \circ \: f)(0) = 17[/tex]
Hope this helps you
