Consider the following statements :
S 1 : Number of points where f(x) = | x sgn (1 – x 2 ) | is non-differentiable is 3.
S 2 : Defined f(x) = 
, In order that f(x) be continuous at x = 0, 'a' should be equal to 
S 3 : The set of all points, where the function 
is differentiable is (– ∞ , 0) ∪ (0, ∞ )
S 4 : Number of points where f(x) = 
is non-differentiable in the interval (0, 3 π ) is 3.
State, in order, whether S 1 , S 2 , S 3 , S 4 are true or false
Text Solution
Verified by ExpertsA
S 1 : f(x) = |x sgn (1 – x 2 )| = 
function is discontinous at x = –1, 1
and non differentiable at x = –1, 0,1
S 2 : f(x) = a sin 
(x + 1) , x 0 = 
, x > 0
a = 
= 
= 
∴ a = 
S 3 : f(x) = (x 2 |x|) 1/3 = 
= – x
f(x) is differentiable every where except at x = 0
S 4 : 
f(x) will be non differentiable if sin –1 (sinx) = 0 or graph of f(x) has a sharp point. Hence number of points of non differentiable will be 5.
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