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Prove that the Greatest Integer Function f : R → R, given b...

Prove that the Greatest Integer Fu | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

Question:

Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-one nor onto, where [x] denotes the greatest integer less than or equal to x.

Answer:

f: R → R is given by,

f(x) = [x]

It is seen that f(1.2) = [1.2] = 1, f(1.9) = [1.9] = 1.

∴ f(1.2) = f(1.9), but 1.2 ≠ 1.9.

∴ f is not one-one.

Now, consider 0.7 ∈ R.

It is known that f(x) = [x] is always an integer. Thus, there does not exist any element x ∈ R such that f(x) = 0.7.

∴ f is not onto.

Hence, the greatest integer function is neither one-one nor onto.

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Comments

Athar Mujtaba Wani
2019-02-23 21:11:43

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Welcome to the NCERT Solutions for Class 12 Mathematics - Chapter . This page offers a step-by-step solution to the specific question from Excercise 2 , Question 3: Prove that the Greatest Integer Function f : R → R, given by f(x) = [x], is neither one-o....

Prove that the Greatest Integer Fu | Class 12 Mathematics Chapter Relations and Functions, Relations and Functions NCERT Solutions

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