Question

ANDEStep 4 of 4: Find:((1)Enable Zoom/Pan8)-2x - 370016) 3x + 2

Answer 1

Hello there. To solve this question, we'll have to remember some properties about rational functions.

Given the functions:

`f(x)=3x+2`

And

`g(x)=-2x-3`

We have to evaluate

`\left((f)/(g)\right)(1)`

For this, remember that:

`\left((f)/(g)\right)(x)=(f(x))/(g(x)),g(x)\text{ not equal to 0}`

The domain of this function is the entire real line, without the point x such that g(x) = 0.

In this case, we'll have

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

Evaluating it at x = 1, we get

`\left((f)/(g)\right)(1)=(3\cdot1+2)/(-2\cdot1-3)=(3+2)/(-2-3)=(5)/(-5)=-1`

This is the value we've been looking for.