A couple quick questions about functions?

Question

If f is a function, does f(s+t)=f(s) +f(t)

If X1f(X2)

Answer 1

For the first question, the answer is NO.

Consider the function, f(x) = x + 1, as a counterexample.

Then f(s+t) = (s+t) + 1, however, f(s) + f(t) = s + 1 + t + 1 = s + t + 2. So, they are not equal.

For the 2nd question, it is true. Think what is means:

If, x1 < x2, and the curve only goes down from left to right, then the y-value for x1 is going to be higher (greater) than the y-value for x2. In other words, f(x1) > f(x2).

Answer 2

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Answer 3

no. let f(x) = x². then f(s+t) = (s+t)² = s² + 2st + t² <> s² + t² = f(s) + f(t)

yes, that's what "decreasing function" MEANS.