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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Functions

NDA 2017 · Mathematics · Functions

The function f: X arrow Y defined by f(x)= x , where x ∈ X , is...

The function f:X→Yf: \mathrm{X} \rightarrow \mathrm{Y} defined by f(x)=cos⁡xf(\mathrm{x})=\cos \mathrm{x}, where x∈X\mathrm{x} \in \mathrm{X}, is one-one and onto if X and Y are respectively equal to

Options

  1. A[0,π][0, \pi] and [−1,1][-1,1]
  2. B[−π2,π2]and⁡[−1,1]\left[-\frac{\pi}{2}, \frac{\pi}{2}\right] \operatorname{and}[-1,1]
  3. C[0,π][0, \pi] and (−1,1)(-1,1)
  4. D[0,π][0, \pi] and [0,1][0,1]

Correct answer

A. [0,π][0, \pi] and [−1,1][-1,1]

Step-by-step solution

Observe the \cos x graph in the figure.
It is clear that, function is one - one and onto when x and y are [0,π][0, \pi] and [−1,1][-1,1]
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