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

2. Постройте график функции: \( \begin{array}{ll}\text { a) } y=\sqrt{x-1}-1 ; & \text { в) } y=-4(x-2)^{2}-1 \\ \text { б) } y=\frac{4}{x-5}-1 ; & \end{array} \)

1. \( f(x)=x+\frac{1}{x} \rightarrow f(1), f(-1), f(2), f\left(\frac{1}{2}\right) \)

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 \( t=2\pi \)).

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

(d) \( \sqrt{1+x^{2}} \)