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Chapter 1: Problem 20
The sum of two numbers is \(50 .\) Express the product of the numbers, \(P,\) as a function of one of the numbers, \(x .\)
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Define a piecewise function on the intervals \((-\infty, 2],(2,5)\) and \([5, \infty)\) that does not "jump" at 2 or 5 such that one piece is a constant function, another piece is an increasing function, and the third piece is a decreasing function.
$$\text { Solve and check: } \frac{x-1}{5}-\frac{x+3}{2}=1-\frac{x}{4}$$
Explain how to find the difference quotient of a function \(f\) \(\frac{f(x+h)-f(x)}{h},\) if an equation for \(f\) is given.
Determine whether each statement makes sense or does not make sense, and explain your reasoning.I used a function to model data from 1990 through 2015 . The independent variable in my model represented the number of years after \(1990,\) so the function's domain was \(\\{x | x=0,1,2,3, \dots, 25\\}\).
The regular price of a computer is \(x\) dollars. Let \(f(x)=x-400\) and \(g(x)=0.75 x\) a. Describe what the functions \(f\) and \(g\) model in terms of the price of the computer. b. Find \((f \circ g)(x)\) and describe what this models in terms of the price of the computer. c. Repeat part (b) for \((g \circ f)(x)\) d. Which composite function models the greater discount on the computer, \(f^{\circ}\) g or \(g \circ f\) ? Explain.
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