Let I be an interval of the real line, that is to say, let I be a line somewhere on the line from negative infinity to positive infinity. Also let I be a subset of the domain of g (a function). It can be said that g is decreasing on I if and only if for all x,y that is an element of I, if x < y then g(x) > g(y).

Prove that g is decreasing on the set of real numbers where g(x)= 2 - 5x

Suppose that x < y then 5x < 5y and therefore 2-5x > 2-5y, and thus g(x) > g(y), so f is decreasing on the interval I and the set of real numbers.

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