For which values of a, f(x)= a(x+sinx) is an increasing function ?

The correct answer is Option (3) → $a\in [0, ∞)$

$f(x)= a(x+\sin x)$

$f'(x)=a(1+\cos x)$ (always ≥ 0)

as $\cos x∈[-1,1]$

$⇒1+\cos x∈[0,2]$

$⇒a∈[0,∞)$ for $f'(x)≥ 0$