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:

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

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 }

$Domain=\lbrace x\ne0\}$