# Given that f(x) = sqrtx - 3 and g(x) = 2x + 1, how do you find (f/g)(-sqrt3)?

Oct 2, 2017

See a solution process below:

#### Explanation:

First, we can write $\left(\frac{f}{g}\right) \left(x\right)$ as:

$\left(\frac{f}{g}\right) \left(x\right) = \frac{\sqrt{x} - 3}{2 x + 1}$

To find $\left(\frac{f}{g}\right) \left(- \sqrt{3}\right)$ we need to substitute $\textcolor{red}{- 3}$ for each occurrence of $\textcolor{red}{x}$ in $\left(\frac{f}{g}\right) \left(x\right)$:

$\left(\frac{f}{g}\right) \left(\textcolor{red}{x}\right) = \frac{\sqrt{\textcolor{red}{x}} - 3}{2 \textcolor{red}{x} + 1}$ becomes:

$\left(\frac{f}{g}\right) \left(\textcolor{red}{- \sqrt{3}}\right) = \frac{\sqrt{\textcolor{red}{- \sqrt{3}}} - 3}{\left(2 \cdot \textcolor{red}{- \sqrt{3}}\right) + 1}$

(f/g)(color(red)(-sqrt(3))) = (sqrt(color(red)(-sqrt(3))) - 3)/((-2color(red)(sqrt(3)) + 1)