Question

If f(x) = x + cosx – a then ______.

Options

• f(x) is an increasing function

• f(x) is a decreasing function

• f(x) = 0 has one positive root for a < 1

• f(x) = 0 has no positive root for a > 1

Answer 1

If f(x) = x + cosx – a then f(x) is an increasing function.

Explanation:

f(x) = x + cosx – a

Differentiating w.r.t.x, we get

f'(x) = 1 – sinx – 0

f'(x) = 1 – sinx

Which is increasing as –1 ≤ sin x ≤ 1