what is greatest integer function and write the domain and range
Answers
Answer:
The greatest integer functionis defined for all real numbers. Hence, as per its definition, itsdomain is the set of real numbers.
Step-by-step explanation:
If you want a proof, go back to the basics. What is the domain? Set of points where the function is well defined. To say gif is well defined at some x , we need to say-
There are some integers smaller than x .
The set of such integers achieves it's supremum.
Based on construction/axioms of real numbers, try to see how both these hold for all real numbers.
As for the range, y is in the range of gif if there is some x in the domain of gif for which gif(x)=y . As we are concerned with finding the greatest integer, notice how the range will be a subset of integers. To say any integer y is in range, can you find a corresponding x ? That will wrap up your proof.