Question

A train is traveling 55 mph to a destination that is 330 mi away. The function f(x)=−55x+330f(x)=−55x+330 represents the remaining number of miles to the destination after x hours of travel. What is the practical domain of the function f?

Answer 1

F(x) = - 55x + 330

The domain is the set of possible input-values, i.e. x-values.

You know that f(x) cannot bebigger than 330 not lower than zero, then construct the inequality:

0 ≤ f(x) ≤ 330

0 ≤ - 55x + 330 ≤ 330

Multilply by - 1 and change the inequality signs:

0 ≥ 55x - 330 ≥ -330

Add 330 to all the members

330 ≥ 55x ≥ 0

Divide by 55

6 ≥ x ≥ 0 => 0 ≤ x ≤ 6

The the possible x-values (practical domain) is all the real numbers between 0 and 6 inclusive.