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Chapter 1: Problem 27

Evaluate each function at the given values of the independent variable and simplify. \(f(x)=4 x+5\) a. \(f(6)\) b. \(f(x+1)\) c. \(f(-x)\)

Short Answer

Expert verified
The answers to the exercise are: \(f(6) = 29\), \(f(x+1) = 4x + 9\), and \(f(-x) = -4x + 5\).

Step by step solution

01

Evaluate \(f(6)\)

The given value \(6\) is to be substituted into the function \(f(x)\). This is restated as \(f(6) = 4 * 6 + 5\). Simplifying this, you get \(f(6) = 29\).
02

Evaluate \(f(x+1)\)

The given expression \(x+1\) is substituted in place of \(x\) in the function \(f(x)\). Consequently, \(f(x+1) = 4(x+1) + 5 = 4x + 4 + 5 = 4x + 9\). This form is simplified, hence no further simplification is needed.
03

Evaluate \(f(-x)\)

The given expression \(-x\) is substituted in place of \(x\) in the function \(f(x)\). Thus, \(f(-x) = 4(-x) + 5 = -4x + 5\). This form is simplified, hence no further simplification is possible here.

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