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Chapter 8: Problem 1
Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(1,2),(3,4),(5,5)\\}$$
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Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=3 x-7 \text { and } g(x)=\frac{x+3}{7}$$
Find \(f(g(x))\) and \(g(f(x))\) and determine whether each pair of functions \(f\) and \(g\) are inverses of each other. $$f(x)=4 x+9 \quad \text { and } \quad g(x)=\frac{x-9}{4}$$
Find a. \((f \circ g)(x)\), b. \((g \circ f)(x)\), c. \((f \circ g)(2)\). $$f(x)=\frac{1}{x}, \quad g(x)=\frac{2}{x}$$
Find a. \((f \circ g)(x)\), b. \((g \circ f)(x)\), c. \((f \circ g)(2)\). $$f(x)=\frac{1}{x}, \quad g(x)=\frac{1}{x}$$
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 \(f^{-1}(f(x))=x\). $$f(x)=x+5$$
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