Question

Find two functions F and G such that (f°g) (x) = h (x). In the picture are the Function

Answer 1

The Solution:

The question says that

$\begin{gathered} f(g(x))=h(x) \\ \text{and} \\ \\ h(x)=\frac{1}{x+2} \end{gathered}$

We are asked to find the two functions; f(x) and g(x).

$\begin{gathered} \text{ If }f(g(x))=h(x)=\frac{1}{x+2} \\ \text{Then it follows that} \\ g(x)=x+2 \\ \text{and} \\ f(x)=\frac{1}{x} \end{gathered}$

Therefore, the correct answers are:

$f(x)=\frac{1}{x}\text{ and g(x)=x+2}$