The range of the function y = (1/2 - sin3 x) for real x is :

Question

The range of the function y = (1/2 - sin3 x) for real x is : (A) (1/3) le y le 1 (B)  - (1/3) le y le 1 (C)  - (1/3) le y > 1 (D)  - (1/3) > y > 1

Tardigrade Admin · Accepted Answer

We know - 1 le sin x le 1 Cubing both sides, we get - 1 le sin3 x le 1 Multiply by - ve, we get 1 ge - sin3 x ge -1 Add 2 on each side 3 ge 2 - sin3 x ge 1 Take reciprocal on each side, we get (1/3) le (1/2 - sin3 x) le1 ⇒ (1/3) le y le1 (∵ y = (1/2- sin3x))

Q. The range of the function $y = \frac{1}{2 - s i n ^{3} x}$ for real x is :

$\frac{1}{3} \leq y \leq 1$

$- \frac{1}{3} \leq y \leq 1$

$- \frac{1}{3} \leq y > 1$

$- \frac{1}{3} > y > 1$

Q. The range of the function y=2−sin3x1​ for real x is :

31​≤y≤1

−31​≤y≤1

−31​≤y>1

−31​>y>1

We know −1≤sinx≤1 Cubing both sides, we get −1≤sin3x≤1 Multiply by - ve, we get 1≥−sin3x≥−1 Add 2 on each side 3≥2−sin3x≥1 Take reciprocal on each side, we get 31​≤2−sin3x1​≤1 ⇒31​≤y≤1(∵y=2−sin3x1​)

Q. The range of the function $y = \frac{1}{2 - s i n ^{3} x}$ for real x is :

$\frac{1}{3} \leq y \leq 1$

$- \frac{1}{3} \leq y \leq 1$

$- \frac{1}{3} \leq y > 1$

$- \frac{1}{3} > y > 1$