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Chapter 2: Problem 37

Evaluate each function at the given values of the independent variable and simplify. \(f(x)=\frac{x}{|x|}\) a. \(f(6)\) b. \(f(-6)\) c. \(f\left(r^{2}\right)\)

Short Answer

Expert verified
The answers to the function evaluation at specific values are \(f(6)=1\), \(f(-6)=-1\), and \(f\left(r^{2}\right)=1\).

Step by step solution

01

Evaluation of f(6)

When evaluating \(f(6)\), 6 will be substituted for \(x\). Given \(f(x)=\frac{x}{|x|}\), substituting 6 for \(x\) gives: \(f(6)=\frac{6}{|6|}\). The absolute value of 6 is 6, so the function simplifies to: \(f(6)=\frac{6}{6}\) = 1.
02

Evaluation of f(-6)

For \(f(-6)\), -6 is substituted for \(x\). This gives \(f(-6)=\frac{-6}{|-6|}\). The absolute value of -6 is 6, so the function simplifies to: \(f(-6)=\frac{-6}{6}\) = -1.
03

Evaluation of \(f\left(r^{2}\right)\)

When evaluating \(f\left(r^{2}\right)\), \(r^{2}\) is substituted for \(x\). Giving \(f\left(r^{2}\right)=\frac{r^{2}}{|r^{2}|}\). Any square number is positive, so the absolute value of \(r^{2}\) is just \(r^{2}\). The function therefore simplifies to: \(f\left(r^{2}\right)=\frac{r^{2}}{r^{2}}\) = 1.

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