MathDB

The function

f

is increasing and convex (i.e. every straight line between two points on the graph of

f

lies above the graph) and satisfies

f(f(x))=3^x

for all

x\in\mathbb{R}

. If

f(0)=0.5

determine

f(0.75)

with an error of at most

0.025

. The following are corrent to the number of digits given:
3^{0.25}=1.31607, 3^{0.50}=1.73205, 3^{0.75}=2.27951.

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