Question

Find the range of the function f(x) = cot^–1(log_0.5(x⁴ – 2x² + 3)) 

Answer 1

We have (x⁴ – 2x² + 3) = (x² – 1)² + 2 ≥ 2

Let g(x) = (x⁴ – 2x³ + 3) and h(x) = log(x⁴ – 2x² + 3)

Now, R_g = [2, ∞)

and R_h = (log_0.5 (∞), log_0.5 (2)] = (–∞, –1]

Also, Range of cot^–1 x is (0, π) and cot^–1 x is a decreasing function.

Thus, R_f = [cot^–1(–1), π) = [3(π/4), π)