The maximum of the function f(x) = -3x^2-2(k-5)x+ K - 8 is equal to the the minimum of the function g(x) = x^2-2 (k-1)x+ k +7 Find all such functions f and g.
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Answer:
Step-by-step explanation:
f(x−1)+f(x+1)=
3
f(x)
⇒f(x)+f(x+2)=
3
f(x+1)
Putting, x=x+2,
f(x+1)+f(x+3)=
3
f(x+2)
f(x−1)+2f(x+2)+f(x+3)=
3
[
3
f(x+1)]
f(x−1)+f(x+3)=f(x+1)
Putting, x=x+2, again
f(x+1)+f(x+5)=f(x+3)
f(x−1)+f(x+5)=0
f(x+5)=−f(x−1)
f(x)=−f(x+6)
f(x+12)=f(x)
∑
r−0
19
f(5+12r)=20f(5)=20×10=200
Hence, sum of digits =2+0+0=2
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