Algebra Examples

$f (x) = {\begin{cases} 3 - 5 x & x \leq 3 \\ 3 x & 3 < x < 7 \\ 5 x + 1 & x \geq 7 \end{cases}$ , $f (5)$

Step 1

Identify the piece that describes the function at $x = 5$ . In this case, $x = 5$ falls within the interval $3 < x < 7$ , therefore use $3 x$ to evaluate $f (5)$ .

$f (x) = {\begin{cases} 3 - 5 x & x \leq 3 \\ 3 x & 3 < x < 7 \\ 5 x + 1 & x \geq 7 \end{cases}$

Step 2

The function is equal to $3 x$ at $x = 5$ .

$f (x) = 3 x]_{x = 5}^{}$

Step 3

Evaluate the function at $x = 5$ .

$f (5) = 3 (5)$

Step 4

Multiply $3$ by $5$ .

$f (5) = 15$