Question

f(x)=\

$$\begin{cases}x^3 - 6x, & x \\leq -3\\\\-4, & -3 < x \\leq 3\\\\\\sqrt{3x - 3}, & x > 3\\end{cases}$$

evaluate f(4)

Explanation:

Step1: Determine the applicable piece of the function

Since \( 4 > 3 \), we use the third piece of the piecewise function, which is \( f(x)=\sqrt{3x - 3} \).

Step2: Substitute \( x = 4 \) into the function

Substitute \( x = 4 \) into \( \sqrt{3x - 3} \):
\[

$$\begin{align*} f(4)&=\sqrt{3(4)-3}\\ &=\sqrt{12 - 3}\\ &=\sqrt{9}\\ &= 3 \end{align*}$$

\]

Answer:

\( 3 \)