Let \f(x) = \{ \table x\sin(1/x),\when x \neq0;1,\when x= 0 and A = {x ∊ R : f(x) = 1}. Then A has

Correct Answer is : exactly one element

KVPY 2019 SB SX Exam Previous Papers

Question : 7 of 120

Marks: +1, -0

Let

\f(x) = \{ \table x\sin(1/x),\when x ≠0;1,\when x= 0

and A = {x ∊ R : f(x) = 1}. Then A has

Solution:

f(x) = 1 for x = 0
for x ≠ 0, f(x) = 1
⇒

x \sin1/x-1

⇒

\sin1/x=1/x

⇒ sinθ = θ which is true only when θ = 0
As θ ≠ 0 so it is not possible

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