The Solution:
The question says that
[tex]\begin{gathered} f(g(x))=h(x) \\ \text{and} \\ \\ h(x)=\frac{1}{x+2} \end{gathered}[/tex]
We are asked to find the two functions; f(x) and g(x).
[tex]\begin{gathered} \text{ If }f(g(x))=h(x)=\frac{1}{x+2} \\ \text{Then it follows that} \\ g(x)=x+2 \\ \text{and} \\ f(x)=\frac{1}{x} \end{gathered}[/tex]
Therefore, the correct answers are:
[tex]f(x)=\frac{1}{x}\text{ and g(x)=x+2}[/tex]
