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Problem 167

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

Expert verified

We have calculated the function values: \(f(2) = 0\), \(f\left(\frac{1}{2}\right) = -1\), and \(f\left(\frac{-3}{4}\right) = -11\).

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Chapter 9

Find the relation \(Q\) over \(\mathrm{S} \times \mathrm{T}\) if \(\mathrm{S}=\\{1,2,3\\}, \mathrm{T}=\\{4,5\\}\), and the rule of correspondence is \(\mathrm{r}(\mathrm{x})=\mathrm{x}+2\).

Chapter 9

Show that the inverse of the function $\mathrm{y}=\mathrm{x}^{2}+4 \mathrm{x}-5$ is not a function.

Chapter 9

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) \(\mathrm{f}(\mathrm{x})=\mathrm{x}^{2}+1\).

Chapter 9

Which of the following sets are functions of \(\mathrm{x}\) ? $$ \begin{aligned} &\mathrm{A}=\\{(5,1),(4,2),(4,3),(6,4)\\} \\ &\mathrm{B}=\\{(\mathrm{x}, \mathrm{y})|\mathrm{y}=| \mathrm{x} \mid\\}, \quad \mathrm{C}=\\{(\mathrm{x}, \mathrm{y})|\mathrm{x}=| \mathrm{y} \mid\\} ? \end{aligned} $$

Chapter 9

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 \(\mathrm{h}(2)\)

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