Mark the correct alternative in each of the following: Let f: R → R be given by f(x) = [x] 2 + [x + 1]–3, where [x] denotes the greatest integer less than or equal to x. Then, f(x) is

Question

Philoid · Accepted Answer

Given that f: R → R be given by f(x) = [x]² + [x + 1] – 3

As [x] is the greatest integer so for different values of x, we will get same value of f(x).

[x]² + [x + 1] will always be an integer.

So, f is many-one.

Similarly, in this function co domain is mapped with at most one element of domain because for every x ϵ R, f(x) ϵ Z.

So, f is into.

Mark the correct alternative in each of the following:Let f: R → R be given by f(x) = [x]2 + [x + 1]–3, where [x] denotes the greatest integer less than or equal to x. Then, f(x) is

Mark the correct alternative in each of the following:
Let f: R → R be given by f(x) = [x]² + [x + 1]–3, where [x] denotes the greatest integer less than or equal to x. Then, f(x) is