Answer:
3 is not in the domain of [tex]f\circ g[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=\sqrt{x+5}[/tex]
[tex]g(x)=-4x+4[/tex]
We need to check whether 3 is in the domain of [tex]f\circ g[/tex] or not.
[tex]f\circ g=f(g(x))[/tex]
[tex]f\circ g=f(-4x+4)[/tex] [tex][\because g(x)=-4x+4][/tex]
[tex]f\circ g=\sqrt{(-4x+4)+5}[/tex] [tex][\because f(x)=\sqrt{x+5}][/tex]
[tex]f\circ g=\sqrt{-4x+9}[/tex]
This function is defined if
[tex]-4x+9\geq 0[/tex]
[tex]9\geq 4x[/tex]
[tex]\dfrac{9}{4}\geq x[/tex]
It means domain of the function [tex]f\circ g[/tex] is [tex](-\infty,\dfrac{9}{4}][/tex].
[tex]3\notin (-\infty,\dfrac{9}{4}][/tex]
Therefore, 3 is not in the domain of [tex]f\circ g[/tex].
