$$ \left. \begin{array} { l } { f ( x ) = \left\{ \begin{array} { l r } { 2 x ^ { 3 } - 1 , } & { x

Question

$$ \left. \begin{array} { l } { f ( x ) = \left\{ \begin{array} { l r } { 2 x ^ { 3 } - 1 , } & { x < 1 } \ { 3 , } & { 1 \leq x < 5 } \ { | x - 2 | , } & { x \geq 5 } \end{array} ight.} \ { f ( 8 ) = } \ { f ( 0 ) = } \ { } \end{array} ight. $$

UpStudy AI · Accepted Answer

Let's evaluate the piecewise function $$ f(x) $$ at the specified points.

The function is defined as:
$$
f(x) = 
\begin{cases} 
2x^3 - 1 & \text{if } x < 1 \
3 & \text{if } 1 \leq x < 5 \
|x - 2| & \text{if } x \geq 5 
\end{cases}
$$

### 1. Calculate $$ f(8) $$:

- **Determine the applicable case:**
  
  Since $$ 8 \geq 5 $$, we use the third case: $$ f(x) = |x - 2| $$.

- **Compute $$ f(8) $$:**
  $$
  f(8) = |8 - 2| = |6| = 6
  $$

**Thus, $$ f(8) = 6 $$.**

### 2. Calculate $$ f(0) $$:

- **Determine the applicable case:**
  
  Since $$ 0 < 1 $$, we use the first case: $$ f(x) = 2x^3 - 1 $$.

- **Compute $$ f(0) $$:**
  $$
  f(0) = 2(0)^3 - 1 = 0 - 1 = -1
  $$

**Thus, $$ f(0) = -1 $$.**

### Summary:
$$
\begin{align*}
f(8) &= 6 \
f(0) &= -1
\end{align*}
$$
$$ f(8) = 6 $$ and $$ f(0) = -1 $$.

\( \left. \begin{array} { l } { f ( x ) = \left\{ \begin{array} { l r } { 2 x ^ { 3 } - 1 , } & { x < 1 } \\ { 3 , } & { 1 \leq x < 5 } \\ { | x - 2 | , } & { x \geq 5 } \end{array} \right.} \\ { f ( 8 ) = } \\ { f ( 0 ) = } \\ { } \end{array} \right. \)

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