Find domain of inverse sine function - jelet 2024 - jelet previous year question solution by sandip sir jelet academy
Problem: 1: Find domain of inverse sine function Solution: **Assumptions:** * The function is defined over real numbers. * Standard definitions of inverse trigonometric functions and logarithms are used. 1. **Identify Domain Restrictions:** The function is $f(x) = \sin^{-1} \left( \log_2 \left( \frac{x^2}{2} \right) \right)$. For $f(x)$ to be defined, two conditions must be met: * The argument of the inverse sine function must be in the interval $[-1, 1]$. * The argument of the logarithm function must be strictly positive. 2. **Apply Logarithm Domain Condition:** The argument of $\log_2$ is $\frac{x^2}{2}$. $\frac{x^2}{2} > 0$ This implies $x^2 > 0$, which means $x \ne 0$. 3. **Apply Inverse Sine Domain Condition:** The argument of $\sin^{-1}$ is $\log_2 \left( \frac{x^2}{2} \right)$. $-1 \le...