Show me greatest integer function is neither one one nor onto
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Hey friend,Harish here.
Here is your answer:
Let the greatest integer function be:
f : R → R, Which is given by,
f(x) = [x]
We know that: f(1.5) = [1.5] = 1 ; f(1.6) = [1.6] = 1.
∴ f(1.5) ≠ f(1.6) & f is not one to one function.
Now, Let 0.5 ∈ R.
We know that,
f(x) = [x] is always an integer. Thus, there does not exist any an element x ∈ R such that f(x) = 0.5.
∴ f is also not onto.
Hence the greatest integer function is neither one - one, nor onto.
____________________________________________________
Hope my answer is helpful to you.
Here is your answer:
Let the greatest integer function be:
f : R → R, Which is given by,
f(x) = [x]
We know that: f(1.5) = [1.5] = 1 ; f(1.6) = [1.6] = 1.
∴ f(1.5) ≠ f(1.6) & f is not one to one function.
Now, Let 0.5 ∈ R.
We know that,
f(x) = [x] is always an integer. Thus, there does not exist any an element x ∈ R such that f(x) = 0.5.
∴ f is also not onto.
Hence the greatest integer function is neither one - one, nor onto.
____________________________________________________
Hope my answer is helpful to you.
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