Question

find the for (f/g)(x) and simplify the answer .then find the domain for (f/g)(x) then round answer to two decimal places if necessary

Answer 1

`\begin{gathered} (f(x))/(g(x))=\frac{5x\cdot\sqrt[]{x-1}}{x-1} \\ \text{Domain(f/g)(x)}=x>1\text{ or (1,}\infty) \end{gathered}`

Step by step explanation:

We have to find the division of the functions:

`\begin{gathered} f(x)=5x \\ g(x)=\sqrt[]{x-1} \\ ((f)/(g))(x)=(f(x))/(g(x)) \end{gathered}`

Then, by the division we get:

`(f(x))/(g(x))=\frac{5x}{\sqrt[]{x-1}}`

To solve the division, we have to multiply by the conjugated:

`\begin{gathered} (f(x))/(g(x))=\frac{5x\cdot\sqrt[]{x-1}}{\sqrt[]{x-1}\cdot\sqrt[]{x-1}} \\ (f(x))/(g(x))=\frac{5x\cdot\sqrt[]{x-1}}{x-1} \end{gathered}`

Since the function can only take a number greater than 1 because we need a number different from zero on the denominator and no negative values on the roots.