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

ANDEStep 4 of 4: Find:((1)Enable Zoom/Pan8)-2x - 370016) 3x + 2-example-1
User Spectral Instance
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1 Answer

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27 votes

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.

User Stasi
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