f-x-2-x-2f-x-2-3x-2-9x-2-15x-then-what-is-the-value-of-f-10-

Question Number 23833 by Joel577 last updated on 07/Nov/17

f (x^{2} + x) + 2 f (x^{2} - 3 x + 2) = 9 x^{2} - 15 x

then what is the value of f (10) ?

Commented by prakash jain last updated on 07/Nov/17

x = 0

f (0) + 2 f (2) = 0

x = 1

f (2) + 2 f (0) = - 6

f (2) = 2

f (0) = - 4

f (x) is linear function

f (x) = a x + b

\Rightarrow f (x) = 3 x - 4

f (x^{2} + x) + 2 f (x^{2} - 3 x + 2) =

= 3 (x^{2} + x) - 4 + 2 [3 (x^{2} - 3 x + 2) - 4]

= 3 x^{2} + 3 x - 4 + 2 (3 x^{2} - 9 x + 2)

= 9 x^{2} - 15 x

f (x) = 3 x - 4

f (10)

= 30 - 4 = 26

Commented by ajfour last updated on 07/Nov/17

y o u m a k e i t e a s y e n o u g h s i r!

Commented by Joel577 last updated on 08/Nov/17

t h a n k y o u v e r y m u c h

Answered by kaivan.ahmadi last updated on 13/Dec/17

f (0) = - 4 az the Mr parkash slution

if we set x^{2} + x = 10 \Rightarrow

x^{2} - 3 x + 2 = - 4 x + 12

and

{9 x}^{2} - 15 x = - 24 x + 90

Now replace

f (10) + 2 f (- 4 x + 12) = - 24 x + 90

and so for x = 3 we have

f (10) + 2 f (0) = 18 \Rightarrow f (10) = 26

in this way we didnt use the

linearly of f .

Commented by prakash jain last updated on 13/Dec/17

Thanks . It is a good approach .

Very useful when it is difficult

to evaluate f (x) in terms of x alone .