Precalculus Examples

f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}

$f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}$ Find

f (3)

$f (3)$

Step 1

Identify the piece that describes the function at

x = 3

$x = 3$ . In this case,

x = 3

$x = 3$ falls within the interval

x = 3

$x = 3$ , therefore use

2

$2$ to evaluate

f (3)

$f (3)$ .

f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}

$f (x) = {\begin{cases} {(x - 3)}^{2} - 2 & x \neq 3 \\ 2 & x = 3 \end{cases}$

Step 2

The function is equal to

2

$2$ at

x = 3

$x = 3$ .

f (x) = 2 (]_{x = 3}^{})

$f (x) = 2 (]_{x = 3}^{})$

Step 3

Evaluate the function at

x = 3

$x = 3$ .

f (3) = 2

$f (3) = 2$