11. Sydney bought a new car for $32,000.00

To find the value of the car after three years, we can use the given equation:

\[
f(x) = 32,000(0.92)^x
\]

For \(x = 3\):

\[
f(3) = 32,000(0.92)^3
\]

First, calculate \(0.92^3\):

\[
0.92^3 = 0.778688
\]

Now, substituting this value back into the equation:

\[
f(3) = 32,000 \times 0.778688
\]

Calculating that:

\[
f(3) = 32,000 \times 0.778688 = 24,000.00 + 24,000.00 \times 0.778688 = 24,000.00 + 18,000.00 + 12,000.00 + 8,000.00 + 4,000.00 = 24,992 + 262 = 24,992.00 + 262.04 = 24,992.00 + 2,962.00 = 24,992.00 + 2,962.00 = 24,992
\]

After performing the multiplication, we find the final value:

\[
f(3) = 24,991.00
\]

So, the value of the car after three years, rounded to the nearest cent, is:

\[
\text{The value of the car after three years is } \$24,991.00.
\]