Question:
At $ x=\frac{3}{2} $ the function $ f(x)=\frac{|2x-3|}{2x-3} $ is
At $ x=\frac{3}{2} $ the function $ f(x)=\frac{|2x-3|}{2x-3} $ is
Updated On: Jun 23, 2024
- continuous
- discontinuous
- differentiable
- non-zero
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The Correct Option is B
Solution and Explanation
Given, $ f(x)=\frac{|2x-3|}{2x-3} $
$ \left\{ \begin{matrix} \frac{2x-3}{2x-3}, & if & x\ge \frac{3}{2} \\ \frac{-(2x-3)}{2x-3}, & if & x
$ \left\{ \begin{matrix} \frac{2x-3}{2x-3}, & if & x\ge \frac{3}{2} \\ \frac{-(2x-3)}{2x-3}, & if & x
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Concepts Used:
Continuity
A function is said to be continuous at a point x = a, if
limx→a
f(x) Exists, and
limx→a
f(x) = f(a)
It implies that if the left hand limit (L.H.L), right hand limit (R.H.L) and the value of the function at x=a exists and these parameters are equal to each other, then the function f is said to be continuous at x=a.
If the function is undefined or does not exist, then we say that the function is discontinuous.
Conditions for continuity of a function: For any function to be continuous, it must meet the following conditions:
- The function f(x) specified at x = a, is continuous only if f(a) belongs to real number.
- The limit of the function as x approaches a, exists.
- The limit of the function as x approaches a, must be equal to the function value at x = a.