91Ó°ÊÓ

Let the domain of \(\mathrm{M}=\\{(\mathrm{x}, \mathrm{y}): \mathrm{y}=\mathrm{x}\) ) be the set of real numbers. Is M a function?

if \(\mathrm{f}(\mathrm{x})=(\mathrm{x}-2) /(\mathrm{x}+1)\), find the function values \(\mathrm{f}(2), \mathrm{f}(1 / 2)\) and \(\mathrm{f}(-3 / 4)\).

If \(g(x)=x^{2}-2 x+1\), find the given element in the range, (a) \(\mathrm{g}(-2)\) (b) \(g(0)\) (c) \(g(a+1)\) (d) \(\mathrm{g}(\mathrm{a}-1)\)

Find the domain \(D\) and the range \(R\) of the function \((x, x /|x|)\)

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

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 \(\mathrm{f}(\mathrm{x})=3 \mathrm{x}-5\).

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 \(\mathrm{t}\)

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, \(\mathrm{C}\) ) and \(g(x)=x-5\) with \(D_{g}=R(\) or \(C)\). Find (a) \(\mathrm{f}+\mathrm{g}\) (b) \(\mathrm{f}-\mathrm{g}\) (c) \(\mathrm{fg}\) (d) \(\mathrm{f} / \mathrm{g}\).