Question

f(x)=\

$$\begin{cases} 3x^3 - 1, & x < 1 \\\\ 3, & 1 \\leq x < 4 \\\\ |x - 1|, & x \\geq 4 \\end{cases}$$

evaluate f(-2)
type answer here.

Explanation:

Step1: Determine the applicable piece

Since \(-2 < 1\), we use the first piece of the piece - wise function \(f(x)=3x^{3}-1\).

Step2: Substitute \(x = - 2\) into the function

Substitute \(x=-2\) into \(f(x)=3x^{3}-1\). We know that \(x^{3}=(-2)^{3}=-8\) (because \((-2)\times(-2)\times(-2)=-8\)). Then \(3x^{3}=3\times(-8)=-24\). Then \(f(-2)=3\times(-2)^{3}-1=-24 - 1\).

Step3: Calculate the result

\(-24-1=-25\).

Answer:

\(-25\)