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

Options

A. 7
B. 8
C. 9
D. 10

Answer

C

Explanation

`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`