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Chapter 7: Problem 46

Evaluate each function at the given value of the variable. \(f(x)=\frac{|x|}{x}\) a. \(f(5)\) b. \(f(-5)\)

Short Answer

Expert verified
The function evaluated at \(x=5\) and \(x=-5\) is \(f(5)=1\) and \(f(-5)=-1\), respectively.

Step by step solution

01

Substitute \(x=5\) in the function

First, substitute \(x = 5\) in the function, so the function becomes \(f(5)=\frac{|5|}{5}\). The absolute value of \(5\) is \(5\), therefore, \(f(5)=\frac{5}{5}\).
02

Simplify \(\frac{5}{5}\) to get \(f(5)\)

The fraction \(\frac{5}{5}\) simplifies to \(1\). Hence, \(f(5) = 1\).
03

Substitute \(x=-5\) in the function

Next, substitute \(x = -5\) in the function, so the function becomes \(f(-5)=\frac{|-5|}{-5}\). The absolute value of \(-5\) is \(5\), therefore, \(f(-5)=\frac{5}{-5}\).
04

Simplify \(\frac{5}{-5}\) to get \(f(-5)\)

The fraction \(\frac{5}{-5}\) simplifies to \(-1\). Hence, \(f(-5) = -1\).

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