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If f(x^2-6x+6)+f(x^2-4x+4)=2x ,AA x in R...

If `f(x^2-6x+6)+f(x^2-4x+4)=2x ,AA x in R` then `f(-3) + f(9) -5f(1)= ?` (A) 7 (B) 8 (C) 9 (D) 10

A

7

B

8

C

9

D

10

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(2)-6x+6=x^(2)-4x+4 rArr x=1`
Put x = 1 in the given relation to get
f(1) = 1
for `x^(2)-6x+6=1, x = 1 or 5`
for `x^(2)-4x+4=1, x =1or 3`
Put x = 3 and 5 in the given relation to get
`f(-3)+f(1)=6rArrf(-3)=5`
`and f(1)+f(9)=10 rArr f(9)=9`
`therefore" "f(-3)+f(9)-5f(1)=9`
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