Math, asked by kmanoharan045, 11 months ago

what is greatest integer function and write the domain and range​

Answers

Answered by dhanushree7552
0

Answer:

The greatest integer functionis defined for all real numbers. Hence, as per its definition, itsdomain is the set of real numbers.

Answered by yoginisoni
0

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.

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