The function \(f : R \to R\) given by \(f(x) = 3x - \sin 2x\) is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → strictly increasing on R
Differentiating:
\( f'(x) = 3 - 2\cos 2x \)
Since \(\cos 2x \le 1\) for every x, \(2\cos 2x \le 2\), so
\( f'(x) \ge 3 - 2 = 1 \gt 0 \) for all real x
The derivative is positive everywhere, so f is strictly increasing on R. This also rules out the other three options.