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  • Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 17 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 8 Continuity Exercise 8.1 Question 17 Maths Textbook Solution.

Answers (1)

Answer:

                Discontinuous

Hint:

For a function to be continuous at a point, its LHL RHL and value at that point should be equal.

Solution:

Given,

                f(x)=\left\{\begin{array}{l} 2 x-1, \text { if } x<0 \\\\ 2 x+1, \text { if } x \geq 0 \end{array}\right.

We observe

[LHL at x=0 ]

                \lim _{x \rightarrow 0^{-}} f(x)=2(0)-1=-1

[RHL at x=0 ]

                \begin{aligned} &\lim _{x \rightarrow 0^{+}} f(x)=2(0)+1=1 \\ &\lim _{x \rightarrow 0^{+}} f(x) \neq \lim _{x \rightarrow 0^{-}} f(x) \end{aligned}

Thus,  f\left ( x \right ) is discontinuous at x=0 .

 

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