Question

F(x) = 3x + 2; g(x) = 3x - 5 Find f/g.

Answer 1

Answer:

$(\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}$ for $x\neq \dfrac{5}{3}$.

Step-by-step explanation:

The given functions are

$f(x)=3x+2$

$g(x)=3x-5$

We need to find the function $(\dfrac{f}{g})(x)$.

Using division property of functions.

$(\dfrac{f}{g})(x)=\dfrac{f(x)}{g(x)}$

Substitute the values of functions.

$(\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}$

This function is defined for all values of x, except a value for which 3x-5=0.

$3x-5=0\Rightarrow x=\dfrac{5}{3}$

Therefore, the required function is $(\dfrac{f}{g})(x)=\dfrac{3x+2}{3x-5}$ for $x\neq \dfrac{5}{3}$.

Answer 2

$\left(\dfrac{f}{g}\right)(x)=\dfrac{3x+2}{3x-5}$