Question

Find the range of

f(x) = 3cot^-1x + 2tan^-1x + π/4

Answer 1

We have

f(x) = 2(tan^-1x + cot^-1x) + cot^-1x + π/4

= 2.π/2 + cot^-1x + π/4

= cot^-1x + 5π/4

Also, 0 < cot^-1x < π

⇒5π/4 < cot^-1x + 5π/4 < π + 5π/4

⇒ 5π/4 < f(x) < 9π/4

Thus, R_f = (5π/4, 9π/4)