To find the value of the car after three years using the equation \( f(x) = 32,000(0.92)^x \), we will substitute \( x = 3 \) into the equation.
\[ f(3) = 32,000(0.92)^3 \]
First, calculate \( (0.92)^3 \):
\[ (0.92)^3 = 0.778688 \]
Next, substitute this value back into the function:
\[ f(3) = 32,000 \times 0.778688 \]
Now, perform the multiplication:
\[ f(3) = 32,000 \times 0.778688 \approx 24,973.99936 \]
Rounding to the nearest cent, the value of the car after three years is:
\[ \text{Value of the car} \approx 24,974.00 \]
Therefore, the value of the car after three years is $24,974.00.