Respuesta :

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]

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