$$ 1 \leftarrow\left\{\begin{array}{ll}3 x-2 & ext { if }-3 \leq x \leq 4 \ x^{3}-4 & ext { if } 4

Question

$$ 1 \leftarrow\left\{\begin{array}{ll}3 x-2 & 	ext { if }-3 \leq x \leq 4 \ x^{3}-4 & 	ext { if } 4

UpStudy AI · Accepted Answer

To solve the problem, we need to evaluate the piecewise function defined as:

$$
f(x) = 
\begin{cases}
3x - 2 & \text{if } -3 \leq x \leq 4 \
x^3 - 4 & \text{if } 4 < x \leq 6
\end{cases}
$$

We will evaluate $$ f(x) $$ for the specified values of $$ x $$.

### (a) $$ f(0) $$

Since $$ 0 $$ falls within the interval $$ -3 \leq x \leq 4 $$, we use the first piece of the function:

$$
f(0) = 3(0) - 2 = -2
$$

### (b) $$ f(1) $$

Since $$ 1 $$ also falls within the interval $$ -3 \leq x \leq 4 $$, we again use the first piece of the function:

$$
f(1) = 3(1) - 2 = 3 - 2 = 1
$$

### (c) $$ f(4) $$

Since $$ 4 $$ is at the boundary of the first interval $$ -3 \leq x \leq 4 $$, we use the first piece of the function:

$$
f(4) = 3(4) - 2 = 12 - 2 = 10
$$

### (d) $$ f(6) $$

Since $$ 6 $$ falls within the interval $$ 4 < x \leq 6 $$, we use the second piece of the function:

$$
f(6) = 6^3 - 4 = 216 - 4 = 212
$$

### Summary of Results

- (a) $$ f(0) = -2 $$
- (b) $$ f(1) = 1 $$
- (c) $$ f(4) = 10 $$
- (d) $$ f(6) = 212 $$

Thus, the answers are:
- (a) $$ f(0) = -2 $$
- (b) $$ f(1) = 1 $$
- (c) $$ f(4) = 10 $$
- (d) $$ f(6) = 212 $$
$$ f(0) = -2 $$, $$ f(1) = 1 $$, $$ f(4) = 10 $$, $$ f(6) = 212 $$.

\( 1 \leftarrow\left\{\begin{array}{ll}3 x-2 & \text { if }-3 \leq x \leq 4 \\ x^{3}-4 & \text { if } 4

Ask by Ray Daniel. in the United States

Mar 19,2025

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\( 1 \leftarrow\left\{\begin{array}{ll}3 x-2 & \text { if }-3 \leq x \leq 4 \\ x^{3}-4 & \text { if } 4 Ask by Ray Daniel. in the United States Mar 19,2025