Answer: [tex]g(x)= x+6[/tex]
Step-by-step explanation:
Given functions are: [tex]f(x)= 4\sqrt{x+1}[/tex] and [tex]h(x)= 4\sqrt{x+7}[/tex]
So, [tex](f\circ g)(x)=f[g(x)]= 4\sqrt{g(x)+1}[/tex] (Replacing [tex]x[/tex] as [tex]g(x)[/tex] in the given [tex]f(x)[/tex] expression)
Given that, [tex]h(x)=(f\circ g)(x)[/tex] . So, we will get.........
[tex]4\sqrt{x+7}= 4\sqrt{g(x)+1}\\ \\ \sqrt{x+7}= \sqrt{g(x)+1}\\ \\ x+7=g(x)+1\\ \\ g(x)=x+7-1 = x+6[/tex]
Thus, the answer will be: [tex]g(x)= x+6[/tex]
