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Chapter 8: Problem 6
Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(-7,-7),(-5,-5),(-3,-3),(0,0)\\}$$
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Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. If \(\left(\frac{f}{g}\right)(a)=0,\) then \(f(a)\) must be 0
Use a graphing utility to graph each function. Use the graph to determine whether the function has an inverse that is a function (that is, whether the function is one-to-one). $$f(x)=\frac{x^{3}}{2}$$
The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=\frac{2 x-3}{x+1}$$
The functions are all one-to-one. For each function, a. Find an equation for \(f^{-1}(x),\) the inverse function. b. Verify that your equation is correct by showing that \(f\left(f^{-1}(x)\right)=x\) and \(f^{-1}(f(x))=x\). $$f(x)=3 x-1$$
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x-7 \text { and } g(x)=\frac{x+3}{7}$$
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