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Chapter 7: Q. 7. 115 (page 728)

Given the function R(x)=x鈭�2x+4find the values of x that make the function less than or equal to 0.

Short Answer

Expert verified

The value ofxis(-4,2].

Step by step solution

01

Step 1. Given Information

The given function isR(x)=x鈭�2x+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−2x+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鈭�2x+4鈮�0x鈮�-4

03

Step 3. We have to find the critical points.

x-2=0x+4=0x=2x=-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鈭�2x+4

x=1is1鈭�21+4=-15

x=-1is -1鈭�2-1+4=-1

x=4is 4鈭�24+4=14

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

(-4,2]

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