Question

f(x)=\

$$\begin{cases}\\frac{2}{x + 4},&x < -4\\\\x,&-4 \\leq x \\leq 0\\\\x^4 - 6,&x > 0\\end{cases}$$

evaluate f(-4)

Explanation:

Step1: Determine the applicable piece

We need to find which piece of the piece - wise function \(f(x)\) is applicable when \(x = - 4\). The piece - wise function is defined as:
\(f(x)=

$$\begin{cases}\frac{2}{x + 4},&x\lt - 4\\x,&-4\leq x\leq0\\x^{4}-6,&x\gt0\end{cases}$$

\)
Since \(-4\) satisfies the inequality \(-4\leq x\leq0\), we use the piece \(f(x)=x\) for \(x=-4\).

Step2: Evaluate the function

Substitute \(x = - 4\) into the function \(f(x)=x\) (the applicable piece). So, \(f(-4)=-4\).

Answer:

\(-4\)