KVPY2019MathematicsFunctions
Let f x = x sin 1 x   when   x ≠ 0 1   when   x = 0 and A = x ∈ R : f x = 1 Then, A has
Options
- Aexactly one element
- Bexactly two elements
- Cexactly three elements
- Dinfinitely many elements
Correct answer
A. exactly one element
Step-by-step solution
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.