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Chapter 8: Problem 4
Determine whether each relation is a function. Give the domain and range for each relation. $$\\{(5,6),(5,7),(6,6),(6,7)\\}$$
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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). $$f(x)=x^{3}+x+1$$
Find a. \((f \circ g)(x)\), b. \((g \circ f)(x)\), c. \((f \circ g)(2)\). $$f(x)=\frac{1}{x}, \quad g(x)=\frac{1}{x}$$
Describe how to use the graph of a one-to-one function to draw the graph of its inverse function.
Let $$\begin{array}{l}f(x)=2 x-5 \\\g(x)=4 x-1 \\\h(x)=x^{2}+x+2\end{array}$$. Evaluate the indicated function without finding an equation for the function. $$g(f[h(1)])$$
Find a. \((f \circ g)(x)\), b. \((g \circ f)(x)\), c. \((f \circ g)(2)\). $$f(x)=4 x-3, \quad g(x)=5 x^{2}-2$$
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