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Question

# Let f(x)={−2,−3≤x≤0x−2,x<x≤3 and g(x)=f(|x|)+|f(x)|Which of the following statements are correct?1. g(x) is continuous at x=0.2. g(x) is continuous at x=2.3. g(x) is continuous at x=−1.Select the correct answer using the code given below

A
1 and 2 only
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B
2 and 3 only
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C
1 and 3 only
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D
1, 2 and 3
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Solution

## The correct option is C 1, 2 and 3at x=0,limx→0+g(x)=limx→0+f(|x|)+|f(x)|=−2+2=0limx→0−g(x)=limx→0−f(|x|)+|f(x)|=−2+2=0Hence, it is continuous at x=0.At x=2,limx→2+g(x)=limx→2+f(|x|)+|f(x)|=0limx→2−g(x)=limx→2−f(|x|)+|f(x)|=0Hence, the function is continuous at x=2At x=−1,limx→−1+g(x)=limx→−1+f(|x|)+|f(x)|=−1+2=1limx→−1−g(x)=limx→−1−f(|x|)+|f(x)|=−1+2=1Hence, the function is continuous at x=−1

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