Question

Find the formula for (fog)(x) and simplify your answer. Then find the domain for (fog)(x). Round your answer to two decimal places, if necessary.

Answer 1

(f o g) (x) means put the whole function, g(x), into x of f(x).

Let's do it:

`\begin{gathered} f(x)=(1)/(x) \\ (\text{fog)(x)}=(1)/((x+3)/(2))=(2)/(x+3) \end{gathered}`

The graph of this function looks like:

The domain is the set of x values for which the graph of the function is defined for.

Here, you see x = -3 is not included, otherwise the graph is defined for all other values

So the domain would be:

Domain = { x not equal 0 }

`Domain=\lbrace x\\e0\}`