Question

The equation x + cos x = a has exactly one positive root. Complete set of values of 'a' is

• A. (0, 1)
• B. (-∞, 1)
• C. (-1, 1)
• D. ) (1, ∞)

Answer 1

)

Sol. Let f(x) = x + cosx - a

⇒ f '(x) = 1 − sinx ≥ 0 ∀ x ∈ R. Thus f(x) is increasing in

(-∞, ∞), as zero of f '(x) don't for an interval. f(0) = 1 – 1.

For a positive root 1 − a < 0 ⇒ a > 1