To determine the area of the rectangle given the functions for its length and width, we can follow these steps:
1. Identify the given functions:
- [tex]\( f(x) = x + 3 \)[/tex] (This represents the length of the rectangle)
- [tex]\( g(x) = 6x - 5 \)[/tex] (This represents the width of the rectangle)
2. Substitute [tex]\( x = 3 \)[/tex] into the functions to find the specific length and width:
- Length: [tex]\( f(3) = 3 + 3 = 6 \)[/tex]
- Width: [tex]\( g(3) = 6(3) - 5 = 18 - 5 = 13 \)[/tex]
3. Calculate the area of the rectangle:
- The area [tex]\( A \)[/tex] of a rectangle is given by multiplying the length by the width:
[tex]\[
A = \text{length} \times \text{width}
\][/tex]
- Substitute the values we found:
[tex]\[
A = 6 \times 13 = 78
\][/tex]
Therefore, the area of the rectangle is [tex]\( 78 \)[/tex]. The correct choice is:
78
