The range of the function f(x) = x/|x| isA. R – {0} B. R – {-1, 1

1.	The range of the function f(x) = x/\|x\| isA. R – {0} B. R – {-1, 1} C. {-1, 1} D. None of these
Answer» Option : (C) Given, f(x) = x/\|x\| We know that, \|x\| = -x in (-∞, 0) and \|x\| = x in [0, ∞) So, f(x) = \(\frac{x}{-x}\) = -1 in (-∞, 0) And f(x) = \(\frac{x}{-x}\) in (0, ∞) As clearly shown above f(x) has only two values 1 and -1 So, Range of f(x) = {-1, 1}

The range of the function f(x) = x/|x| isA. R – {0} B. R – {-1, 1} C. {-1, 1} D. None of these

Answer»

Option : (C)

Given,

f(x) = x/|x|

We know that,

|x| = -x in (-∞, 0) and

|x| = x in [0, ∞)

So,

f(x) = \(\frac{x}{-x}\)

= -1 in (-∞, 0)

And f(x) = \(\frac{x}{-x}\) in (0, ∞)

As clearly shown above f(x) has only two values 1 and -1

So,

Range of f(x) = {-1, 1}