Answer:
[tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex] for [tex]x\neq \dfrac{5}{3}[/tex].
Step-by-step explanation:
The given functions are
[tex]f(x)=3x+2[/tex]
[tex]g(x)=3x-5[/tex]
We need to find the function [tex](\dfrac{f}{g})(x)[/tex].
Using division property of functions.
[tex](\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}[/tex]
Substitute the values of functions.
[tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex]
This function is defined for all values of x, except a value for which 3x-5=0.
[tex]3x-5=0\Rightarrow x=\dfrac{5}{3}[/tex]
Therefore, the required function is [tex](\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}[/tex] for [tex]x\neq \dfrac{5}{3}[/tex].
