Respuesta :

carlosego

For this case we have the following functions:

[tex]f (x) = x ^ 2\\g (x) = x-3[/tex]

We must find[tex](g_ {0} f) (x)[/tex]

By definition we have to:

[tex](g_ {0} f) (x) = g (f (x))[/tex]

So:

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

We must evaluate the composite function for [tex]x = -2[/tex]

[tex]g (f (-2)) = (- 2) ^ 2-3 = 4-3 = 1[/tex]

ANswer:

[tex]g (f (-2)) = 1[/tex]

kudzordzifrancis

ANSWER

1

EXPLANATION

The given functions are:

[tex]f(x) = {x}^{2} [/tex]

and

[tex]g(x) = x - 3[/tex]

[tex](g \circ \: f)(x) = f(g(x))[/tex]

[tex](g \circ \: f)(x) = g( {x}^{2} )[/tex]

[tex](g \circ \: f)(x) = {x}^{2} - 3[/tex]

We substitute x=-2 to obtain;

[tex](g \circ \: f)( - 2) = {( - 2)}^{2} - 3[/tex]

We simplify to obtain:

[tex](g \circ \: f)( - 2) = 4- 3[/tex]

[tex](g \circ \: f)( - 2) = 1[/tex]

The first choice is correct.

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