Question

question
$f(x)=\

$$\begin{cases}\\frac{4}{3}x + 4&\\text{for } -6 < x < 0\\\\x + 5&\\text{for } 0 \\leq x \\leq 4\\end{cases}$$

$
find $f(0)$
answer

Explanation:

Step1: Determine the applicable piece of the function

We need to find \( f(0) \). Looking at the piecewise function, for \( x = 0 \), we use the second piece \( f(x)=x + 5 \) since the domain for this piece is \( 0\leq x\leq4 \) and \( 0 \) is included in this domain.

Step2: Substitute \( x = 0 \) into the applicable function

Substitute \( x = 0 \) into \( f(x)=x + 5 \). So we have \( f(0)=0 + 5 \).

Step3: Calculate the result

Simplify \( 0+5 \) to get \( 5 \).

Answer:

\( 5 \)