Answer:
g(x) = x + 3
Step-by-step explanation:
A composite function is a function that is written inside another function which means substituting one function into another function.
Ex: (fоg)(x) is a composite function, where x of f(x) is substituted by g(x)
∵ h(x) = (fоg)(x)
∵ [tex]h(x)=\sqrt{x+5}[/tex]
∵ [tex]f(x)=\sqrt{x+2}[/tex]
→ Substitute x of f(x) by g(x)
∴ (fоg)(x) = [tex]\sqrt{g(x)+2}[/tex]
→ Equate (fоg)(x) by h(x)
∴ [tex]\sqrt{g(x)+2}=\sqrt{x+5}[/tex]
→ Cancel the roots from the two sides
∴ g(x) + 2 = x + 5
→ Subtract 2 from both sides
∴ g(x) + 2 - 2 = x + 5 - 2
∴ g(x) = x + 3
