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f(x) = x2 + 3; g(x) = Square root of quantity x minus two.

Find f(g(x)).

f(g(x)) = (x2 + 3)(Square root of quantity x minus two.)
f(g(x)) = Square root of quantity x minus two divided by quantity x squared plus three.
f(g(x)) = x + 1
f(g(x)) = Square root of quantity x squared plus three.

Respuesta :

bluplanet18
f(x) = x^2 + 3
g(x) = sqrt(x - 2)

f(g(x)) = x - 2 + 3 = x + 1

Answer:

The correct option is 3.

Step-by-step explanation:

The given functions are

[tex]f(x)=x^2+3[/tex]

[tex]g(x)=\sqrt{x-2}[/tex]

We need to find the value of f(g(x)).

[tex]f(g(x))=f(\sqrt{x-2})[/tex]            [tex][\because f(x)=x^2+3][/tex]          .... (1)

Substitute [tex]x=\sqrt{x-2}[/tex] in function f(x) to find the value of [tex]f(\sqrt{x-2})[/tex].

[tex]f(\sqrt{x-2})=(\sqrt{x-2})^2+3[/tex]

[tex]f(\sqrt{x-2})=x-2+3[/tex]

[tex]f(\sqrt{x-2})=x+1[/tex]

Substitute the value of [tex]f(\sqrt{x-2})[/tex] in equation (1).

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

Therefore, the correct option is 3.

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