Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \{- | x |,- \sqrt{ 1- x^2} \}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :
- Three elements
- One element
- Five elements
- Two elements
The Correct Option is A
Solution and Explanation
$f(x) = \text{max} \{- | x | , - \sqrt{1 - x^2 } \}$
Non-derivable at $3$ points in $(-1, 1)$
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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.