Question

Let $f:R\to R$ be defined as $f\left(x\right)=\frac{sin\pi \left\{x\right\}}{x^2-x+1}\forall xϵR$, where {x} is the fractional part of x, then

• A. f is neither even nor odd function
• B. f is a zero function
• C. f is many-one and non-constant function
• D. f is one-one function

Answer 1

Answer: (A), (C)

The correct options are
A f is neither even nor odd function
C f is many-one and non-constant function

$f\left(x\right)=\frac{sin\pi (-x-[-x\left]\right)}{x^2-x+1}andf(-x)=\frac{sin\pi (-x-[-x\left]\right)}{x^2+x+1}$
$\therefore$ f(x) is neither even nor odd, also at integers f(x) = 0
f(x) is many one function.