Discussion

Explanation:

Given, f(x) = $\frac{\mathrm{x}}{\left|\mathrm{x}\right|}$

Case 1: x > 0
⇒ |x| = x
∴ f(x) = $\frac{\mathrm{x}}{\mathrm{x}}$ = 1

Case 2: x < 0
⇒ |x| = - x
∴ f(x) = $\frac{\mathrm{x}}{-\mathrm{x}}$ = - 1

∴ f(x) = 1 when x > 0 while f(x) = -1 when x < 0.

⇒ f(x) can take only two values {1, -1}.

Hence, option (b).

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