Answer: The value of g(x) is x+3.
Step-by-step explanation:
Since we have given that
[tex]h(x)=f\circ g(x)[/tex]
Here,
[tex]h(x)=\sqrt{x+5}\\\\and\\\\f(x)=\sqrt{x+2}[/tex]
We need to find the value of g(x):
[tex]f(x)=\sqrt{x+2}\\\\f(g(x))=\sqrt{g(x)+2}\\\\h(x)=\sqrt{g(x)+2}\\\\\sqrt{x+5}=\sqrt{g(x)+2}\\\\x+5=g(x)+2\\\\g(x)=x+5-2=x+3[/tex]
Hence, the value of g(x) is x+3.
