Question

If the range of the function f(x) = cot^-1(x²/(x² + 1)) is (a, b), find the value of (b/a + 2)

Answer 1

Let g(x) = x²/(x² + 1) = 1 - 1/(1 + x²)

Cleary, R_g =[0, 1)

Now, R_f = (f(1), f(0)] = (cot^-1(1), cot^-1(1)]

= (π/4, π/2]

Hence, the value of (b/a + 2)

= ((π/2)/(π/4) + 2) = 2 + 2 = 4