Explanation-Why-While-f-ax-b-f-cx-d-ex-g-then-f-x-Ax-2-Bx-C-

Question Number 194190 by tri26112004 last updated on 29/Jun/23

E x p l a n a t i o n W h y :

W h i l e f (a x + b) + f (c x + d) = e x + g

t h e n f (x) = {A x}^{2} + B x + C ¿

Commented by Tinku Tara last updated on 30/Jun/23

For the given condition it is not

necessary for f (x) to be quadratic .

f (x) = A x + B

f (a x + b) = A a x + A b + B

f (c x + d) = A c x + A d + B

g = A (b + d) + 2 B

e = A (a + c)

A = \frac{e}{a + c}

B = g - \frac{e (b + d)}{(a + c)}