Respuesta :

Answer:

Option D is correct.

[tex]f(x) = 4x^2[/tex]

[tex]g(x) = x+1[/tex]

Step-by-step explanation:

As per the statement:

If [tex]h(x) = (fog)(x)[/tex] and [tex]h(x) = 4(x+1)^2[/tex]

Find: f(x) and g(x).

[tex]h(x) = (f(g(x))[/tex]

[tex]4(x+1)^2=f(g(x))[/tex]

From the options

let [tex]g(x) = x+1[/tex] and [tex]f(x) = 4x^2[/tex]

then;

[tex]f(g(x)) = f(x+1)[/tex]

Replace x with x+1 in f(x) we have;

[tex]f(g(x)) = f(x+1) = 4(x+1)^2[/tex]

Therefore, one  possibility for f(x) and g(x) is:

[tex]f(x) = 4x^2[/tex]

[tex]g(x) = x+1[/tex]

zainebamir540

Answer:

Choice D is correct answer.

Step-by-step explanation:

From question statement, we observe that

h(x) = (f*g)(x)  and h(x) = 4(x+1)²

We have to find possibilities for f(x) and g(x).

Comparing above equation,we get

4(x+1)² = f(g(x))

From possibilities,

let g(x) = x+1 and f(x) = 4x²

h(x) = f(g(x)) = f(x+1)

h(x) = 4(x+1)² which is the answer.


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