QuestionGiven functions $f(x)=3x+1$ and $g(x)=5x-9$, find values where $\frac{f}{g}$ is undefined: $-3$, $\frac{1}{3}$, $\frac{9}{5}$, $\frac{5}{9}$.

Studdy Solution
Let's check the other given values of $x$ to see if they make the denominator zero.
For $x = -3$, $g(x) =5(-3) -9 = -15 -9 = -24 \neq0$
For $x = \frac{1}{3}$, $g(x) =5(\frac{1}{3}) -9 = \frac{5}{3} -9 = -\frac{22}{3} \neq0$
For $x = \frac{5}{9}$, $g(x) =5(\frac{5}{9}) -9 = \frac{25}{9} -9 = -\frac{56}{9} \neq0$
So, the function $\frac{f}{g}$ is defined for $x = -3$, $x = \frac{1}{3}$, and $x = \frac{5}{9}$.
Therefore, the only value of $x$ for which $\frac{f}{g}$ is undefined is $x = \frac{9}{5}$.