91Ó°ÊÓ

In Exercises \(61-66,\) write the function as a composite of two functions \(f\) and \(g .\) (More than one answer is correct.) $$f(g(x))=\frac{2}{|x-3|}$$

Salary. A grocery store pays you \(\$ 8\) per hour for the first 40 hours per week and time and a half for overtime. Write a piecewise-defined function that represents your weekly earnings \(E(x)\) as a function of the number of hours worked \(x\). Find the inverse function \(E^{-1}(x) .\) What does the inverse function tell you?

Find the domain of the given function. Express the domain in interval notation. $$q(x)=\sqrt{7-x}$$

A manager hires an employee at a rate of 10 dollars per hour. Write the function that describes the current salary of the employee as a function of the number of hours worked per week, x. After a year, the manager decides to award the employee a raise equivalent to paying him for an additional 5 hours per week. Write a function that describes the salary of the employee after the raise.

Find the domain of the given function. Express the domain in interval notation. $$k(t)=\sqrt{t-7}$$

An oil spill makes a circular pattern around a ship such that the radius in feet grows as a function of time in hours \(r(t)=150 \sqrt{t} .\) Find the area of the spill as a function of time.

Determine whether each statement is true or false. If the graph of \(y=\frac{1}{x}\) is reflected around the \(x\) -axis, it produces the same graph as if it had bech reflected about the \(y\) -axis.

For the functions \(f(x)=x+a\) and \(g(x)=\frac{1}{x-a},\) find \(g \circ f\) and state its domain.

For Exercises 93 and 94, use the following information: The height (in feet) of a falling object with an initial velocity of 48 feet per second launched straight upward from the ground is given by \(h(i)=-16 r^{2}+48 t,\) where \(t\) is time (in seconds). What is the average rate of change of the height as a function of time from \(t=1\) to \(t=2 ?\)

Use a graphing utility to graph a. \(y=\sqrt{x}\) and \(y=\sqrt{0.1 x}\) b. \(y=\sqrt{x}\) and \(y=\sqrt{10 x}\) What is the relationship between \(f(x)\) and \(f(a x)\), assuming that \(a\) is positive?