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Chapter 1: Problem 33
Find the distance between the points. $$ (1,4),(-5,-1) $$
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(a) find the inverse function of \(f\), (b) graph both \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs of \(f\) and \(f^{-1}\), and (d) state the domain and range of \(f\) and \(f^{-1}\). $$ f(x)=-\frac{2}{x} $$
Find a mathematical model for the verbal statement. A varies directly as the square of \(r\).
Use the functions given by \(f(x)=\frac{1}{8} x-3\) and \(g(x)=x^{3}\) to find the indicated value or function. $$ \left(f^{-1} \circ g^{-1}\right)(1) $$
Find a mathematical model for the verbal statement. The gravitational attraction \(F\) between two objects of masses \(m_{1}\) and \(m_{2}\) is proportional to the product of the masses and inversely proportional to the square of the distance \(r\) between the objects.
In direct variation models of the form \(y=k x, k\) is called the _____ of _____ .
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