x = 0 is the smallest x can be. Anything smaller and it wouldn't make any sense because negative time values make no sense.
x = 7 is the largest x can be. Why? Because plugging in x = 7 leads to f(x) = 1575 - 225x f(7) = 1575 - 225*7 f(7) = 1575 - 1575 f(7) = 0 so at year 7, the value is 0 dollars. Any x value larger than 7 will produce negative dollar values, which make no sense.
Another way to get x = 7 is to notice that 1575 - 225x = 0 has the solution x = 7 We'd solve for x like so 1575 - 225x = 0 1575 = 225x 225x = 1575 x = 1575/225 x = 7
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So x = 0 is the smallest x can be and x = 7 is the largest x can be. This means the domain is [tex]0 \le x \le 7[/tex]
