#### Explain solution RD Sharma class 12 chapter Continuity exercise 8.2 question 19 maths

Discontinuous at x = 1/2 , 1 , 2

Hint:

f(x)/g(x) is continuous at every point hen f(x) & g(x) are continuous except

$g(x) \neq 0$

Given:

$f(x)=\frac{1}{t^{2}+t-2}, t=\frac{1}{x-1}$

Explanation:

\begin{aligned} &f(t)=\frac{1}{t^{2}+t-2} \text { where } t=\frac{1}{x-1}\\ &\text { Clearly } t=\frac{1}{x-1} \text { is discontinuous at } \mathrm{x}=1 \end{aligned}

\begin{aligned} &\text { For } \mathrm{x} \neq 1 \text { we have, }\\ &f(t)=\frac{1}{t^{2}+t-2}=\frac{1}{(t+2)(t-1)} \end{aligned}

\begin{aligned} &\text { This is discontinuous at } x=-2 \text { and } \mathrm{t}=1\\ &\text { For } t=-2, t=\frac{1}{x-1} \Rightarrow x=\frac{1}{2}\\ &\text { For } t=1, t=\frac{1}{x-1} \Rightarrow x=2 \end{aligned}

Hence F is discontinuous at

\begin{aligned} x=\frac{1}{2}, x = 1 \text { and } x = 2 \end{aligned}

## Crack CUET with india's "Best Teachers"

• HD Video Lectures
• Unlimited Mock Tests
• Faculty Support