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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 $$f\left(\frac{-3}{4}\right) = -11$$.
See the step by step solution

## 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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