Question

Identify the function f(x) based on the description given below.

1. Its domain is R and range is {-1, 0, 1}

2. f(x) is +ve when x $>$ 0, f(x) is negative when x is less than zero.

3. It is an odd function

4. The graph of the function breaks (discontinuous) at x = 0

• A. Signum function
• B. Absolute value function
• C. sin x
• D.
• E.

Answer 1

The correct option is A

Signum function

We will eliminate the options using the conditions given. Its domain is R and range is {-1, 0, 1}. Options D and E, $\left(\frac{|x|}{x}\right)and\left(\frac{x}{|x|}\right)$, are not defined when x = 0. So these two can't be the answer Range of sin x is [-1, 1]. This includes the values {-1, 0, 1}, but it has other values between -1 and 1. So the range is not same. $\Rightarrow$ sin x can't be the function |x| is the next option. Its range is [0, $\infty$). So |x| can't be the function.

Next option signum function satisfies all the conditions given.