Question

Find the range of

f(x) = 2cos^-1(-x)² - π

Answer 1

We have

f(x) = 2cos^-1(-x²) - π

= 2(π - cos^-1(x²)) - π

= π - 2cos^-1(x²)

As we know that, 0 ≤ cos^-1(x²) ≤ π

⇒ 0 ≤ 2cos^-1(x²) ≤ 2π

⇒ - 2π ≤ -2cos^-1(x²) ≤ 0

⇒ - 2π + π ≤ π - 2cos^-1(x²) ≤ π

⇒ - π ≤ f(x) ≤ π

Thus, r_f = [-π, π]