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Chapter 9: Chapter 9

Problem 167

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

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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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TABLE OF CONTENTS :
TABLE OF CONTENTS

Step 1: Write down the function

We are given the function: \[f(x) = \frac{x-2}{x+1}\]

Step 2: Find f(2)

To find the function value at \(x = 2\), substitute \(x = 2\) into the function. \[f(2) = \frac{2-2}{2+1}\] Now, we simplify the expression: \[f(2) = \frac{0}{3}\] Finally, we can conclude that: \[f(2) = 0\]

Step 3: Find f(1/2)

To find the function value at \(x = 0.5\) or \(\frac{1}{2}\), substitute \(x = \frac{1}{2}\) into the function. \[f\left(\frac{1}{2}\right) = \frac{\frac{1}{2} - 2}{\frac{1}{2} + 1}\] Now, we simplify the expression: \[f\left(\frac{1}{2}\right) = \frac{-\frac{3}{2}}{\frac{3}{2}}\] Finally, we can conclude that: \[f\left(\frac{1}{2}\right) = -1\]

Step 4: Find f(-3/4)

To find the function value at \(x = -0.75\) or \(\frac{-3}{4}\), substitute \(x = \frac{-3}{4}\) into the function. \[f\left(\frac{-3}{4}\right) = \frac{\frac{-3}{4} - 2}{\frac{-3}{4} + 1}\] Now, we simplify the expression: \[f\left(\frac{-3}{4}\right) = \frac{-\frac{11}{4}}{\frac{1}{4}}\] Finally, we can conclude that: \[f\left(\frac{-3}{4}\right) = -11\] To sum up, we have found the function values: \[f(2) = 0\] \[f\left(\frac{1}{2}\right) = -1\] \[f\left(\frac{-3}{4}\right) = -11\]

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Most popular questions from this chapter

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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 \(\mathrm{r}(\mathrm{x})=\mathrm{x}+2\).
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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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