A Function F(x) Is Defined As F(x) = F(x – 2) - X(x + 2) For All Th

1.	A Function F(x) Is Defined As F(x) = F(x – 2) - X(x + 2) For All The Integer Values Of X And F(1) + F(4) = 0. What Is The Value Of F(1) + F(2) + F(3) + F(4) + F(5) + F(6)?
Answer» LET S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6) As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1) f(2) = f(0) - 8 f(3) = f(1) - 15 f(4) = f(2) - 24 = f(0) - 32 f(5) = f(3) - 35 = f(1) - 50 f(6) = f(4) - 48 = f(0) - 80 Put the above values in EQUATION (1), we get S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80 S = 2(f(0) + f(1)) - 153 ------ (2) As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32 Putting this value in equation 2, we get S = 2(32) - 153 = -89 Let S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6) As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1) f(2) = f(0) - 8 f(3) = f(1) - 15 f(4) = f(2) - 24 = f(0) - 32 f(5) = f(3) - 35 = f(1) - 50 f(6) = f(4) - 48 = f(0) - 80 Put the above values in equation (1), we get S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80 S = 2(f(0) + f(1)) - 153 ------ (2) As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32 Putting this value in equation 2, we get S = 2(32) - 153 = -89

A Function F(x) Is Defined As F(x) = F(x – 2) - X(x + 2) For All The Integer Values Of X And F(1) + F(4) = 0. What Is The Value Of F(1) + F(2) + F(3) + F(4) + F(5) + F(6)?

Answer»

LET S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6)

As f(1) + f(4) = 0, therefore S = f(2) + f(3) + f(5) + f(6) ------ (1)

f(2) = f(0) - 8

f(3) = f(1) - 15

f(4) = f(2) - 24 = f(0) - 32

f(5) = f(3) - 35 = f(1) - 50

f(6) = f(4) - 48 = f(0) - 80

Put the above values in EQUATION (1), we get

S = f(0) - 8 + f(1) - 15 + f(1) - 50 + f(0) - 80

S = 2(f(0) + f(1)) - 153 ------ (2)

As we already know f(1) + f(4) = 0 ⇒f(1) + f(0) - 32 = 0 ⇒f(1) + f(0) = 32

Putting this value in equation 2, we get S = 2(32) - 153 = -89

Let S = f(1) + f(2) + f(3) + f(4) + f(5) + f(6)