Calculas! Don't Ignore
Calculus
Level
3
Let f, g : R → R be continuous functions whose graphs do not intersect. Then for which function, the graph lies entirely on one side of the X-axis:
g-f
gf
g+f
f
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1 solution
Since they never intersect, g ( x ) = f ( x ) , for all x .
Therefore, g ( x ) − f ( x ) = 0 .
As g(x)-f(x) is a continuous function, and it never intersects y = 0 → x axis, it will always stay on one side of the x axis.