Precalculus Examples

$f (x) = {\begin{cases} - 3 x - 3 & x < - 2 \\ 6 x - 28 & x \geq 5 \end{cases}$ Find $f (5)$

Step 1

Identify the piece that describes the function at $x = 5$ . In this case, $x = 5$ falls within the interval $x \geq 5$ , therefore use $6 x - 28$ to evaluate $f (5)$ .

$f (x) = {\begin{cases} - 3 x - 3 & x < - 2 \\ 6 x - 28 & x \geq 5 \end{cases}$

Step 2

The function is equal to $6 x - 28$ at $x = 5$ .

$f (x) = 6 x - 28 (]_{x = 5}^{})$

Step 3

Evaluate the function at $x = 5$ .

$f (5) = 6 (5) - 28$

Step 4

Multiply $6$ by $5$ .

$f (5) = 30 - 28$

Step 5

Subtract $28$ from $30$ .

$f (5) = 2$