Question

Find the formula and simplify your answer then find the domain round your answer to two decimal places if necessary

Answer 1

`\begin{equation*} (f\circ g)(x)=(3)/(x+1) \end{equation*}`
`Domain:(-\infty,-1)\cup(-1,\infty)`

Step-by-step explanation:

Given:

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

To find (f o g)(x), we have to substitute x in f(x) with (x + 1)/3 and simplify as seen below;

`\begin{gathered} (f\circ g)(x)=f(g(x))=(1)/((x+1)/(3))=1/(x+1)/(3)=1*(3)/(x+1)=(3)/(x+1) \\ \therefore(f\circ g)(x)=(3)/(x+1) \end{gathered}`

Recall that the domain of a function is the set of input values for which a function is defined.

So to determine the domain of the stated function, we have to equate the denominator to zero and solve for x as seen below;

`\begin{gathered} x+1=0 \\ x=-1 \end{gathered}`

We can see that for the given function to be defined, x must not be equal to -1, so we can go ahead and write the domain of the function in interval notation as;

`Domain:(-\infty,-1)\cup(-1,\infty)`