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Chapter 1: Problem 7
Assume \(f(x)=\frac{x+2}{x^{2}+1}\) for every real number \(x .\) Evaluate and simplify each of the following expressions. \(f(2 a+1)\)
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The exact number of meters in \(y\) yards is \(f(y),\) where \(f\) is the function defined by $$f(y)=0.9144 y$$ (a) Find a formula for \(f^{-1}(m)\). (b) What is the meaning of \(f^{-1}(m) ?\)
Suppose \(f\) and \(g\) are functions, each with domain of four numbers, with \(f\) and \(g\) defined by the tables below: $$\begin{array}{c|c}x & f(x) \\\\\hline 1 & 4 \\\2 & 5 \\\3 & 2 \\\4 & 3\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 2 & 3 \\\3 & 2 \\\4 & 4 \\\5 & 1\end{array}$$ Sketch the graph of \(f^{-1}\).
Suppose \(g\) is the function whose domain is the interval [-2,2] , with \(g\) defined on this domain by the formula $$g(x)=\left(5 x^{2}+3\right)^{7777}$$ Explain why \(g\) is not a one-to-one function.
Show that the sum of two even functions (with the same domain) is an even function.
Suppose \(f\) and \(g\) are functions, each with domain of four numbers, with \(f\) and \(g\) defined by the tables below: $$\begin{array}{c|c}x & f(x) \\\\\hline 1 & 4 \\\2 & 5 \\\3 & 2 \\\4 & 3\end{array}$$ $$\begin{array}{c|c}x & g(x) \\\\\hline 2 & 3 \\\3 & 2 \\\4 & 4 \\\5 & 1\end{array}$$ Give the table of values for \(g \circ g^{-1}\).
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