# Let f(x)=x^2-4 and g(x)=4x, how do you find (f/g)(x)?

Dec 15, 2016

See explanation.

#### Explanation:

To find such a function you have to write an expression using the given operations with the formulas of functions $f$ and $g$ as arguments:

## $\left(\frac{f}{g}\right) \left(x\right) = \frac{{x}^{2} - 4}{4 x}$

The next step is finding the domain of new function.

Both $f$ and $g$ are polynomials therfore are defined for all real numbers, however in $\left(\frac{f}{g}\right)$ $g \left(x\right)$ appears in the denominator. This excludes all zeros of $g \left(x\right)$ from the domain. So $\left(\frac{f}{g}\right)$ is defined for $x \in \mathbb{R} - \left\{0\right\}$