Let f be a strictly increasing function defined on the set of real numbers. For x real and t positive, setg(x,t)=f(x)−f(x−t)f(x+t)−f(x).
Assume that the inequalities2−1<g(x,t)<2
hold for all positive t if x=0, and for all t≤∣x∣ otherwise.
Show that14−1<g(x,t)<14
for all real x and positive t. inequalitiesfunctionalgebra unsolvedalgebra