Chapter 9: Chapter 9

Show that \(f(a)=f(-a)\) if \(f(x)=x^{2}+3\)

Describe the domain and range of the function $\left.\left.\mathrm{f}=(\mathrm{x}, \mathrm{y}) \mid \mathrm{y}=\sqrt{(} 9-\mathrm{x}^{2}\right)\right\\}\( if \)\mathrm{x}\( and \)\mathrm{y}$ are real numbers.

Find the set of ordered pairs \(\\{(x, y)\\}\) if \(y=x^{2}-2 x-3\) and \(\mathrm{D}=\\{\mathrm{x} \mid \mathrm{x}\) is an integer and $1 \leq \mathrm{x} \leq 4\\}$.

If \(\mathrm{f}(\mathrm{x})=3 \mathrm{x}+4\) and $\mathrm{D}=\\{\mathrm{x} \mid-1 \leq \mathrm{x} \leq 3\\}\(, find the range of \)\mathrm{f}(\mathrm{x})$

Find the zeros of the function \(\mathrm{f}\) if $\mathrm{f}(\mathrm{x})=3 \mathrm{x}-5$.

For each of the following functions, with domain equal to the set of all whole numbers, find: (a) \(\mathrm{f}(0)\); (b) \(\mathrm{f}(1)\); (c) \(\mathrm{f}(-1)\) (d) \(\mathrm{f}(2)\) (e) \(\mathrm{f}(-2)\) (1) \(f(x)=2 x^{3}-3 x+4\) (2) \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+1\).

If $\mathrm{y}=\mathrm{f}(\mathrm{x})=\left(\mathrm{x}^{2}-2\right) /\left(\mathrm{x}^{2}+4\right)\( and \)\mathrm{x}=\mathrm{t}+1$, express \(\mathrm{y}\) as a function of t.

If $\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}-\mathrm{x}-3, \mathrm{~g}(\mathrm{x})=\left(\mathrm{x}^{2}-1\right) /(\mathrm{x}+2)$, and \(\mathrm{h}(\mathrm{x})=\mathrm{f}(\mathrm{x})+\mathrm{g}(\mathrm{x})\), find \(\mathrm{h}(2)\)

Let \(\mathrm{f}(\mathrm{x})=2 \mathrm{x}^{2}\) with domain \(\mathrm{D}_{\mathrm{f}}=\mathrm{R}\) (or, alternatively, C) and \(\mathrm{g}(\mathrm{x})=\mathrm{x}-5\) with \(\mathrm{D}_{\mathrm{g}}=\mathrm{R}\) (or \(\left.\mathrm{C}\right)\) Find (a) \(\mathrm{f}+\mathrm{g} \quad\) (b) \(\mathrm{f}-\mathrm{g}\) (c) fg (d) \(\mathrm{f} / \mathrm{g}\).

If \(\mathrm{D}\) a \(\\{\mathrm{x} \mid \mathrm{x}\) is an integer and $-2 \leq \mathrm{x} \leq 1\\}\(, find the function \)\left\\{(\mathrm{x}, \mathrm{f}(\mathrm{x})) \mid \mathrm{f}(\mathrm{x})=\mathrm{x}^{3}-3\right.$ and \(\mathrm{x}\) belongs to \(\left.\mathrm{D}\right\\}\)