Determine the domain of the function : \( f(x)=\ln (x+2)+1 \) A. \( (-\infty, \infty) \) B. \( (-2, \infty) \) C. \( [2, \infty) \) D. \( (-\infty,-2) \cup(2, \infty) \)

Determine the domain of the function : \( f(x)=\ln (x+2)+1 \) A. \( (-\infty, \infty) \) B. \( (-2, \infty) \) C. \( [2, \infty) \) D. \( (-\infty,-2) \cup(2, \infty) \)

10) If \( f(x)=\frac{1}{x-a}+b \), then \( f^{-1}(a)+f(b)= \)

यदि \( g(x) = 2^{x} \), तो इसके इनवर्स फ़ंक्शन की पहचान करें और उसका डोमेन तथा रेंज लिखिए।

The population of a certain species in a protected area can be modeled by the function \( P(t) = 200 + 50 \sin(t) \), where \( t \) is measured in years. Determine the total population increase over one complete cycle (from \( t=0 \) to \( t=2\pi \)).

4. Найдите область определения функции \( y=1-\sqrt{3 t g \frac{x}{2}-\sqrt{3}} \).