Question

Let $f: R \rightarrow R$ such that $f(x)=x^3+2 x^2+7 x+5+3 \sin x-4 \cos x$ be a function then $f(x)$ is

• A. one-one and onto
• B. one-one but not onto
• C. onto but not one-one
• D. neither one-one nor onto

Answer 1

Answer: (A)

$f ( x )= x ^3+2 x ^2+7 x +5+3 \sin x -4 \cos x$ is an onto function
$\Rightarrow f ^{\prime}( x )=3 x ^2+4 x +7+3 \cos x +4 \sin x \geq 3 x ^2+4 x +2>0$
$\Rightarrow f ( x )$ is an one-one function.