Set, Relation and FunctionHard
Question
Given function f : R → R is defined by f(x) = 
.
Which of the following holds good ?
.Which of the following holds good ?
Options
A.f(x) is continuous and differentiable at x = 1
B.f(x) is continuous but not differentiable at x = 1
C.f′(x) is continuous everywhere
D.Range of f(x) is (0, ∞)
Solution
f′(1+) = -1, f′(1-) = - 1
∴ f(x) is differentiable at x = 1 & hence continuous.
f′(x) =
Hence, f′(x) is continuous everywhere.
Also Rf∈ (0, ∞)
∴ f(x) is differentiable at x = 1 & hence continuous.
f′(x) =
Hence, f′(x) is continuous everywhere.
Also Rf∈ (0, ∞)
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