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Chapter 7: Q. 7. 116 (page 728)

Given the function R(x)=x+1x-4find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

The value ofx is[-1,4)

Step by step solution

01

Step 1. Given Information 

The given function isR(x)=x+1x-4

We have to find the values of x that make the function less than or equal to 0.

02

Step 2. The given function is R(x)=x+1x-4

We want the function to be less than or equal to 0.

R(x)鈮�0

Substitute the rational expression for R(x).

x+1x-4鈮�0x鈮�4

03

Step 3. We have to find the critical points.

x+1=0x-4=0x=-1x=4

04

Step 4. Testing of critical points. To test these critical points, we find the value of the expression at different points.

The expression is x+1x-4

x=0is 0+10-4=1-4

x=3is3+13-4=-4

Write the solution in interval notation. Since 4is excluded we, do not include it in the interval.

[-1,4)

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