What is the domain of that inverse function of \( f(x)=3+\sqrt{x-2} \). a) \( [2, \infty) \) b) \( [3, \infty) \) d) \( (-\infty, 3] \) d) \( (-\infty, 2] \)

Question 2 (4 points) What is the domain of the inverse function of the function \( f(x)=3-\sqrt{x+1} \) ? a) \( (-\infty, 3] \) b) \( [-1, \infty) \) c) \( (-\infty,-1] \) d) \( [3, \infty) \)

What is the range of the inverse function of the function \( f(x)=3-\sqrt{x+1} \) ? a) \( (-\infty,-1] \) b) \( [-1, \infty) \) c) \( [3, \infty) \) d) \( (-\infty, 3] \)

What is the domain of the inverse function of the function \( f(x)=3-\sqrt{x} \). 1 ? a) \( (-\infty, 3] \) b) \( [-1, \infty) \) c) \( (-\infty,-1] \) d) \( [3, \infty) \)

(a) Use the vertex formula to find the vertex. \( \begin{array}{ll}\text { (b) Find the intervals where } f \text { is increasing and where } f \text { is } \\ \text { decreasing. } \\ \begin{array}{ll}\text { 47. } f(x)=6-x^{2} & \text { 48. } f(x)=2 x^{2}-2 x+1 \\ \text { 49. } f(x)=x^{2}-6 x & \text { 50. } f(x)=-2 x^{2}+4 x+ \\ \text { 51. } f(x)=2 x^{2}-4 x+1 & \text { 52. } f(x)=-3 x^{2}+x-\end{array}\end{array} \).

The radioactive substance cesium-137 has a half-life of 30 years. The amount \( A(t) \) (in grams) of a sample of cesium-137 remaining after \( t \) years is given by the following exponential function. \[ A(t)=621\left(\frac{1}{2}\right)^{\frac{t}{30}} \] Find the initial amount in the sample and the amount remaining after 80 years. Round your answers to the nearest gram as necessary.