Respuesta :

gmany

[tex]g(x)=2x\\\\h(x)=x^2+4\\\\(h\circ g)(x)=(2x)^2+4=4x^2+4\\\\(h\circ g)(-3)\to\text{put x = -3 to the equation of the function}\\\\(h\circ g)(-3)=4(-3)^2+4=4(9)+4=36+4=40\\\\Answer:\ \boxed{(h\circ g)(-3)=40}[/tex]

DuarteE

Answer:

[tex]\boxed{(h \circ g)(-3) = 40}.[/tex]

Step-by-step explanation:

By the definition of function composition, we have:

[tex](h \circ g)(-3) = h[g(-3)].[/tex]

Since [tex]g(x) = 2x[/tex], we get:

[tex]g(-3)=2\times(-3) = -6.[/tex]

On the other hand, since [tex]h(x) = x^2+4[/tex], we have:

[tex]h[\underbrace{g(-3)}_{=-6}] = h(-6) = (-6)^2 + 4 = 36 + 4 = 40.[/tex]

So we finally get:

[tex]\boxed{(h \circ g)(-3) = 40}.[/tex]

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