Suppose that the functions $$ f $$ and $$ g $$ are defined as follows. $$ f(x)=\frac{x-9}{x+5} \quad g(x)=\frac{x}{x+5} $$ Find $$ \frac{f}{g} $$, Then, give its domain using an interval or union of interval Simplify your answers. $$ \left(\frac{f}{g}\right)(x)= $$ II Domain of $$ \frac{f}{g} $$ :

Question

UpStudy AI · Accepted Answer

Given the functions $$ f(x) = \frac{x-9}{x+5} $$ and $$ g(x) = \frac{x}{x+5} $$, we need to find the function $$ \frac{f}{g} $$ and then determine its domain.

To find $$ \frac{f}{g} $$, we divide the function $$ f(x) $$ by the function $$ g(x) $$:
$$ \frac{f}{g} = \frac{\frac{x-9}{x+5}}{\frac{x}{x+5}} $$

To simplify this expression, we can cancel out the common factor $$ (x+5) $$ in the numerator and denominator:
$$ \frac{f}{g} = \frac{x-9}{x} $$

Therefore, the function $$ \frac{f}{g} $$ is $$ \frac{x-9}{x} $$.

To determine the domain of $$ \frac{f}{g} $$, we need to consider the values of $$ x $$ for which the function is defined. Since the function is a quotient of two functions, it is defined for all values of $$ x $$ except where the denominator is zero.

The denominator of $$ \frac{f}{g} $$ is $$ x $$, so the function is undefined when $$ x = 0 $$.

Therefore, the domain of $$ \frac{f}{g} $$ is all real numbers except $$ x = 0 $$, which can be represented as $$ (-\infty, 0) \cup (0, \infty) $$.
$$ \frac{f}{g}(x) = \frac{x-9}{x} $$ Domain of $$ \frac{f}{g} $$: $$ (-\infty, 0) \cup (0, \infty) $$

Suppose that the functions \( f \) and \( g \) are defined as follows. \[ f(x)=\frac{x-9}{x+5} \quad g(x)=\frac{x}{x+5} \] Find \( \frac{f}{g} \), Then, give its domain using an interval or union of interval Simplify your answers. \( \left(\frac{f}{g}\right)(x)= \) II Domain of \( \frac{f}{g} \) :

Upstudy AI Solution

Answer

Solution

Beyond the Answer

Related Questions

Latest Pre Calculus Questions