Question

Let the function $f:R\to R$ be defined by $f\left(x\right)=2x+sinx$. Then f is

• A. Bijection
• B. Onto only
• C. One one only
• D. Into and many to one

Answer 1

The correct option is A Bijection

$f^{{}^{\prime }}\left(x\right)=2+cosx>0\forall xϵR\Rightarrow 1:1fa$
as $x\to \infty ,f\left(x\right)\to \infty$
and $x\to \infty ,f\left(x\right)\to -\infty \therefore$ Range is R
Hence Bijective