Question

f(x) = \

$$\begin{cases} (x - 9)^2 - 3 & \\text{for } x \ eq 3 \\\\ 4 & \\text{for } x = 3 \\end{cases}$$

find f(6)

Explanation:

Step1: Determine the applicable piece of the function

The function is defined as \( f(x)=

$$\begin{cases}(x - 9)^2-3, & x eq3\\4, & x = 3\end{cases}$$

\). We need to find \( f(6) \). Since \( 6
eq3 \), we use the first piece of the function, \( f(x)=(x - 9)^2-3 \).

Step2: Substitute \( x = 6 \) into the function

Substitute \( x = 6 \) into \( (x - 9)^2-3 \):
First, calculate \( 6 - 9=-3 \).
Then, square the result: \( (-3)^2 = 9 \).
Finally, subtract 3: \( 9-3 = 6 \).

Answer:

\( 6 \)