Consider the function \( f(x)=\sqrt{x-2}+4 \) for the domain \( [2, \infty) \). Find \( f^{-1}(x) \), where \( f^{-1} \) is the inverse of \( f \). Also state the domain of \( f^{-1} \) in interval notation. \( f^{-1}(x)=0 \) for the domain

Simplify \( \frac{8}{\sqrt{6}+2} \)

Write the expression as a sum and/or difference of logarithms. Express powers as factors. \[ \log _{2}\left(\frac{x^{10}}{x-8}\right), x>8 \] \( \log _{2}\left(\frac{x^{10}}{x-8}\right)=\square \) (Simplify your answer.)

The half-life of radium is 1690 years. If 60 grams are present now, how much will be present in 430 years? \( \square \) grams (Do not round until the final answer. Then round to the nearest thousandth as needed.)

What function is the reflection of \( f(x)=|x+2| \) about the \( x \)-axis? \( g(x)=|x-2| \) Non of the other options \( g(x)=|-x+2| \) \( g(x)=-|x-2| \)

determine whether the given quadratic function has a maximum or a minimum value and then find the value. \( y=-x^{2}+6 x-5 \) \( \begin{array}{lll}\text { [A] minimum, } 3 & \text { [B] minimum, } 4 & \text { [C] maximum, } 4\end{array} \quad \) [D] maximum, 3 A \( \begin{array}{ll}\text { B }\end{array} \) \( \begin{array}{l}\text { C }\end{array} \)