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)=(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)=(1)/(x+2) \\ \text{Then it follows that} \\ g(x)=x+2 \\ \text{and} \\ f(x)=(1)/(x) \end{gathered}`

Therefore, the correct answers are:

`f(x)=(1)/(x)\text{ and g(x)=x+2}`