# Given 3-x where x <= 2 and x^2 where x >2, how do you find f(6)?

##### 1 Answer
Jun 10, 2016

The value is $f \left(6\right) = 36$

#### Explanation:

The function is:

$f \left(x\right) = \left\{\begin{matrix}3 - x & x \le 2 \\ {x}^{2} & x > 2\end{matrix}\right.$

The first step of calculating the value of such piecewise function is to find in which interval is the argument located:

Since $6 > 2$, the argument belongs to the second interval, so you have to apply the formula $f \left(x\right) = {x}^{2}$.

$f \left(6\right) = {6}^{2} = 36$