# Given f(x)=sqrt(7x+7) and g(x)=1/x, how do you find (f/g)(x)?

Dec 29, 2016

See below.

#### Explanation:

Given $f \left(x\right) = \sqrt{7 x + 7}$ and $g \left(x\right) = \frac{1}{x}$, you can find the quotient of the two functions:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{\sqrt{7 x + 7}}{\frac{1}{x}}$

When we divide fractions, we know that $\frac{a}{b} \div \frac{c}{d}$, written $\frac{\frac{a}{b}}{\frac{c}{d}}$ is equivalent to $\frac{a}{b} \times \frac{d}{c}$. We can apply this to our rational function. In the numerator, we have $\frac{\sqrt{7 x + 1}}{1}$ and in the denominator, $\frac{1}{x}$.

$\implies \frac{\sqrt{7 x + 1}}{1} \times \frac{x}{1}$

$\implies x \sqrt{7 x + 7}$

You could also factor out $7$ from inside the radical and write the answer as:

$x \sqrt{7 \left(x + 1\right)}$