Question

8.7 use radicals in functions (homework)
score: 0/10 answered: 0/10
question 1
if f(x)=\sqrt{2x - 16}, then f(14)= (leave your answer in exact form. enter dne if the function is undefined or not a real number)

Explanation:

Step1: Substitute x = 14 into the function

Substitute \(x = 14\) into \(f(x)=\sqrt{2x - 16}\), we get \(f(14)=\sqrt{2\times14 - 16}\).

Step2: Calculate the value inside the square - root

First, calculate \(2\times14-16\): \(2\times14-16 = 28 - 16=12\). So \(f(14)=\sqrt{12}\).

Step3: Simplify the square - root

Simplify \(\sqrt{12}=\sqrt{4\times3}\). Since \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\) (\(a = 4\), \(b = 3\)), we have \(\sqrt{4\times3}=\sqrt{4}\cdot\sqrt{3}=2\sqrt{3}\).

Answer:

\(2\sqrt{3}\)