Problem 33 - Precalculus Essentials

Question

Evaluate each function at the given values of the independent variable and simplify. \(f(r)=\sqrt{r+6}+3\) a. \(f(-6)\) b. \(f(10)\) c. \(f(x-6)\)

Step-by-Step Solution

Answer

\(f(-6) = 3\), \(f(10) = 7\), and \(f(x-6) = \sqrt{x} + 3\)

Step 1: Evaluate f(-6)

Substitute -6 for \(r\) in the function. So, \(f(-6) = \sqrt{-6+6} + 3 = \sqrt{0} + 3 = 0 + 3 = 3\)

Step 2: Evaluate f(10)

Substitute 10 for \(r\) in the function. So, \(f(10) = \sqrt{10+6} + 3 = \sqrt{16} + 3 = 4 + 3 = 7\)

Step 3: Evaluate f(x-6)

Substitute \(x-6\) for \(r\) in the function. So, \(f(x-6) = \sqrt{(x-6)+6} + 3 = \sqrt{x} + 3\)