If the function f:R→ R denned by f(x)=[x] where [x] is the greatest integer not exceeding x, for x∈ R then f is

Question

If the function f:R→ R denned by f(x)=[x] where [x] is the greatest integer not exceeding x, for x∈ R then f is (A) even (B) odd (C) neither even nor odd (D) strictly increasing

Tardigrade Admin · Accepted Answer

We know that, a function is said to be even, if

f (- x) = f (x)

and odd, if

f (- x) = - f (x)

and

f (x)

is increasing, if

f^{'} (x) > 0

Here,

f (x)

is not differentiable at

x \in I

and above two cases are also not satisfied by

f (x)

∴

f (x) = [x]

is neither even nor odd.

Q. If the function f:R→R denned by f(x)=[x] where [x] is the greatest integer not exceeding x, for x∈R then f is

even

odd

neither even nor odd

strictly increasing

We know that, a function is said to be even, if f(−x)=f(x) and odd, if f(−x)=−f(x) and f(x) is increasing, if f′(x)>0 Here, f(x) is not differentiable at x∈I and above two cases are also not satisfied by f(x) ∴ f(x)=[x] is neither even nor odd.

Q. If the function $f : R \to R$ denned by $f (x) = [x]$ where $[x]$ is the greatest integer not exceeding x, for $x \in R$ then $f$ is

We know that, a function is said to be even, if
$f (- x) = f (x)$ and odd, if $f (- x) = - f (x)$ and $f (x)$
is increasing, if $f^{'} (x) > 0$
Here, $f (x)$ is not differentiable at
$x \in I$ and above two cases are also not satisfied by $f (x)$
$∴$ $f (x) = [x]$ is neither even nor odd.