Question

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

Answer 1

`\left((f)/(g)\right)(x)=(3x+2)/(3x-5)`

Answer 2

`((f)/(g))(x)=(3x+2)/(3x-5)` for
`x\\eq (5)/(3)`.

Explanation:

The given functions are

`f(x)=3x+2`

`g(x)=3x-5`

We need to find the function
`((f)/(g))(x)`.

Using division property of functions.

`((f)/(g))(x)=(f(x))/(g(x))`

Substitute the values of functions.

`((f)/(g))(x)=(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=(5)/(3)`

Therefore, the required function is
`((f)/(g))(x)=(3x+2)/(3x-5)` for
`x\\eq (5)/(3)`.