Question

8.7 use radicals in functions (homework)
score: 8/10 answered: 9/10
question 10
if $f(x)=sqrt{4x + 3}$, then $f(x + 4)=$

Explanation:

Step1: Substitute \(x + 4\) for \(x\)

Substitute \(x+4\) into \(f(x)=\sqrt{4x + 3}\).
\[f(x + 4)=\sqrt{4(x + 4)+3}\]

Step2: Simplify the expression inside the radical

Expand \(4(x + 4)+3\).
\[

$$\begin{align*} 4(x + 4)+3&=4x+16 + 3\\ &=4x+19 \end{align*}$$

\]
So \(f(x + 4)=\sqrt{4x+19}\)

Answer:

\(\sqrt{4x + 19}\)