Question

How to do this sum?
suppose that f(x)=dx+m,(d&m are real numbers). Given that f(f(f(x))) = 8x+21, what is the value of d+m?
Please help me or give me a hint.

Answer 1

f(x)=dx+m
can u find f(f(x)) =... ?

Answer 2

replace 'x' in f(x) by 'dx+m'

Answer 3

f(f(x))= d^2x +dm+ m
right?
nd f(f(f(x)))=d^3x + d^2m + dm + m

Answer 4

yes.

Answer 5

d^3x + d^2m + dm + m = 8x+21
so
d^3 = 8
comparing the co-efficients of x
so, d=... ?

Answer 6

equating constants
d^2m + dm + m = (d^2+d+1) m = 21

Answer 7

@hartnn thank u so much!!!!

Answer 8

welcome ^_^