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Answer:
f(1/2)=1/168
f(0)=20/399
Step-by-step explanation:
Let's find f(1/2) first.
Given equation is f(x)+20f(1-x)=
let's appply x=1/2
f(1/2)+20f(1-1/2)=
f(1/2)+20f(1/2)=1/8
21f(1/2)=1/8
f(1/2)=1/168.
Now apply x=0
f(0)+20f(1-0)=(0)^3
f(0)+20f(1)=0
f(0)= -20f(1)--(1)
Now apply x=1
f(1)+20f(1-1)=(1)^3
f(1)+20f(0)=1
from (1)
f(1)+20(-20f(1))=1
f(1)-400f(1)=1
-399f(1)=1
f(1)= -1/399--(2)
applying (2) in eq(1) we get
f(0)= -20(-1/399)
f(0)=20/399
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