7. Given the functions f(x) = log₂ (x-1) and g(x) = log₂ (9-x²), c) Determine (f-g)(x). b) State the domain of g(x). d) State the domain of (f - g)(x). Include a clearly labeled number line.

Suppose s(t) is the total number of miles of railroad in the US built by the end of year t. Give an expression for cach of the following, using the function 8. (You don't need to find a formula.) (a) The number of miles of railroad built by the end of 1885. (b) The number of miles of railroad built during 1884. (c) The average number of miles of railroad built per year during the 1890s.

Use a calculator with a yx key or a Λ key to solve: The 1986 explosion at the Chernobyl nuclear power plant in the former Soviet Union sent about 1000 kilograms of radioactive cesium-137 into the atmosphere. The function f(x) = 1000(0.5) x /30 describes the amount, f(x), in kilograms, of cesium-137 remaining in Chernobyl x years after 1986. If even 100 kilograms of cesium-137 remain in Chernobyl’s atmosphere, the area is considered unsafe for human habitation. Find f(80) and determine if Chernobyl will be safe for human habitation by 2066.

Find the inverse of x^2-20x   and find the domain