Find the domain of each function. Write answers using interval notation. $f(x)=\sqrt{\frac{-1}{x^{3}-1}}$

Solve each problem.

Find the half-life of tritium, a radioactive isotope of hydrogen. which decays according to the function $A(t)=A_0 e^{-0.056 t}$, where t is time in years.

Solve each equation. Give irrational solutions as decimals correct to the nearest thousandth. $e^{x^{4}}=1000$

Solve each equation. Give solutions in exact form. $\log _{2}[(x-4)(x-2)]=3$

Solve each equation. $\log _{x} \frac{27}{64}=3$

Solve each problem. Suppose an Egyptian mummy is discovered in which the amount of carbon-14 present is only about one-third the amount found in living human beings. How long ago did the Egyptian die?

Write each equation in logarithmic form. $100^{1 / 2}=10$

For each function that is one-to-one, write an equation for the inverse function. Give the domain and range of both f and $f^{-1}$. If the function is not one-to-one, say so. f(x)=$\frac{2 x-1}{5-3 x}$

For f(x)=$3^x$ and $g(x)=\left(\frac{1}{4}\right)^{x}$, find each of the following. Round answers to the nearest thousandth as needed.

Find the half-life of tritium, a radioactive isotope of hydrogen, which decays according to the function $A(t)=A_{0} e^{-0.056 t}$, where t is time in years.

Solve each equation. Give solutions in exact form. $\log _{2} x+\log _{2}(x+2)=3$

Find each value. If applicable, give an approximation to four decimal places. log 0.0055

For $f(x)=3^{x}$ and $g(x)=\left(\frac{1}{4}\right)^{x}$, find each of the following. Round answers to the nearest thousandth as needed. f(3)

Determine whether each function graphed or defined is one-to-one. $y=\frac{-1}{x+2}$