If it is true explain why is so, if it is false give a counterexample.
2007-10-22 05:08:01 · 5 answers · asked by gigichic21 1 in Science & Mathematics ➔ Mathematics
Sure it's true. IF x1>x2 => f(x1)>f(x2) and g(x1)>g(x2) then adding the inequaliies gives (f+g(x1))>(f+g(x2)) for x1>x2 and the function is increasing. Same if they're both decreasing. It's only when one function is increasing and the other one decreasing that you really have to work for it and show which grows faster ☺
Doug
2007-10-22 05:21:50 · answer #1 · answered by doug_donaghue 7 · 1⤊ 0⤋
Increasing Function
2016-09-30 23:58:24 · answer #2 · answered by luff 4 · 0⤊ 0⤋
An increasing function has a positive slope.
e.g. y=m1x+b1
y=m2x+b2
y=(m1+m2)x+b1+b2
(m1+m2) is positive, so it's increasing?
2007-10-22 05:27:37 · answer #3 · answered by cidyah 7 · 0⤊ 1⤋
it's true
if f(x) and g(x) are increasing that means
x < y => f(x) < f(y) and g(x) < g(y)
just add these two inequalities and you get the result
2007-10-22 05:13:12 · answer #4 · answered by Ivan D 5 · 1⤊ 0⤋
True
f(x), g(x) are increasing:
if x < y then f(x) < f(y) and g(x) < g(y)
f(x) + g(x) < f(y) + g(x)
f(y) + g(x) < f(y) + g(y)
so
f(x) + g(x) < f(y) + g(y)
2007-10-22 05:25:41 · answer #5 · answered by Maria Fontaneda 6 · 0⤊ 0⤋