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Question

Which one of the following graph represents the function \({\rm{f}}\left( {\rm{x}} \right) = \frac{{\rm{x}}}{{\rm{x}}},{\rm{\;x}} \ne 0?\)

This question was previously asked in
NDA I 2017 GAT Previous Year Paper (23-Apr-2017)
The correct answer is

Calculation:

Here, f(x) = y = x/x and x ≠ 0

Now, at y = 1, x ≠ 0

But at x = 0, we get 0/0 (indeterminate form)

So, f(x) = x/x = 1 for all point except x = 0

Hence, option (3) is correct.
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