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  • Please Solve RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 9 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter Continuity Exercise 8.1 Question 9 Maths Textbook Solution.

Answers (1)

Answer:

                x=a  (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}{c} \frac{x-a}{x-a}, \text { if } x>a \\\\ \frac{a-x}{x-a}, \text { if } x<a \\\\ 1 \quad, \text { if } x=a \end{array}\right)   

f(x)=\left(\begin{array}{ll} 1, & x>a \\ -1, & x<a \\ 1, & x=a \end{array}\right)

f(x)=\left(\begin{array}{l} 1, x \geq a \\ -1, x<a \end{array}\right)

We observe

[LHL at x=a ]

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

[RHL at x=a ]

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

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

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