Question

Identify the function f(x) from the description given below.

1. x - 1 $<f\left(x\right)\le x$

2. Its domain is R and Range is I(set of integers)

3. f(x) = 3 $\Rightarrow 3\le x<4$

4. f(x) = -3 $\Rightarrow -3\le x<-2$

• A. Signum function
• B. Greatest integer function
• C. Absolute value function
• D. Least integer function

Answer 1

The correct option is B

Greatest integer function

We will first look at the second condition given. It says the range is set of integers. We know that signum function and absolute value function have different range.

We are now left with greatest integer function and least integer function. Third condition given is f(x) = 3 if 3$\le x<4$. This is true for greatest integer function. For least integer function, f(x) = 4 if 3 $<x\le 4$