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STD 12 - 1. relation and function — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 1. relation and function4 Marks
MCQ
If $f:R \to R$, is a continuous function such that $\left| {f\left( x \right) - f\left( y \right)} \right| \geqslant \left| {{e^x} - {e^y}} \right|\forall x,y \in R$ then $f(x)$ is
  • A
    surjective
  • ✓
    one-one
  • C
    many one
  • D
    periodic
✓

Answer

Correct option: B.
one-one
b
If $x \neq y $ and $ f(x)=f(y) \Rightarrow\left|e^{x}-e^{y}\right| \leq 0$ which is not possible

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