Question

The function$f\left(x\right)=x+\cos x$ is

• A. Always increasing
• B. Always decreasing
• C. Increasing for a certain range of $x$.
• D. None of the above

Answer 1

The correct option is A

Always increasing

Explanation for correct option

$f\left(x\right)=x+\cos x$

$f\text{'}\left(x\right)=1-\sin \left(x\right)$

Now, $\sin \left(x\right)\le 1$

$\therefore 1-\sin \left(x\right)\ge 0$ [$f\left(x\right)>0$ is a condition of increasing function]

Hence, option A is correct .