Let f x = x sin 1 x when x ≠ 0 1 when x = 0 and A = x ∈ R : f x = 1 Then, A has

Question

Let f x = x sin 1 x when x ≠ 0 1 when x = 0 and A = x ∈ R : f x = 1 Then, A has, exactly one element, exactly two elements, exactly three elements, infinitely many elements

MARKS App · Accepted Answer

Given function f x = x sin 1 x , when x ≠ 0 1 , when x = 0 Now, for x = 0 , f x = 1 and for x ≠ 0 , f x = 1 ⇒ sin 1 x = 1 x has no solution. ∴ The set A = x ∈ R : f x = 1 has exactly one element.

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