Область значений функции arccos
D[arccos(2x)] = [0; π], то есть
0 ≤ arccos(2x) ≤ π, ⇔ 0 ≤ 3·arccos(2x) ≤ 3π, ⇔ 0 ≥ -3arccos(2x) ≥ -3π, ⇔
⇔ (π/4) ≥ (π/4) - 3arccos(2x) ≥ (π/4) - 3π = (π - 12π)/4 = -11π/4, ⇔
⇔ -11π/4 ≤ (π/4) - 3arccos(2x) ≤ π/4.
ответ. [-11π/4; π/4].
Область значений функции arccos
D[arccos(2x)] = [0; π], то есть
0 ≤ arccos(2x) ≤ π, ⇔ 0 ≤ 3·arccos(2x) ≤ 3π, ⇔ 0 ≥ -3arccos(2x) ≥ -3π, ⇔
⇔ (π/4) ≥ (π/4) - 3arccos(2x) ≥ (π/4) - 3π = (π - 12π)/4 = -11π/4, ⇔
⇔ -11π/4 ≤ (π/4) - 3arccos(2x) ≤ π/4.
ответ. [-11π/4; π/4].