Question

The dimensions of various-sized mirrors are created using

the expression 0.5x – 2 for the width and 2x + 2 for the
length. The function A(x) = x2 – 3x – 4 represents the area
of the mirrors. The maximum length of the mirrors is 52
centimeters.
How do the mathematical domain and reasonable domain compare.

Answer 1

• mathematical domain (-∞, ∞)
• reasonable domain (4, 25]

Explanation:

Each of the functions is defined for all values of x, so the mathematical domain is "all real numbers."

The width must be greater than 0, and the length is limited to 52 cm, so the restrictions on the reasonable domain are ...

0.5x -2 > 0

x > 4

__

2x +2 ≤ 52

x +1 ≤ 26

x ≤ 25

The reasonable domain is (4, 25] cm. The reasonable domain is a subset of the mathematical domain.