Question

If f(x)=ax+b and f(f(f(x)))=8x+21 what is the value of a+b

Answer 1

------------------------------HEY DEAR---------------------------------

HERE IS YOUR ANSWER........

f(x) = ax +b

f(f(f(x))) = 8x +21

TAKE L.H.S

=>f(f(ax+ b)

means put ax + b in place of x

=>f(a(ax +b) +b)

put a(ax+b) +b in place of x

=> a^2 (ax+b) + ba  +b

=> (a^3)x + b(a^2) + ba +b

ACCORDING TO QUESTION L.H.S = R.H.S

8x +21 = (a^3)x + b(a^2) +ab +b

compare both equations................

(a^3) = 8

so, a = 2

also,   21 = b(4)+ 2b +b

          21 = 7b

           b = 21/7

            b= 3

so, a+b => 2+3    =>     5.....................................Ans.

SO, 5 IS THE ANSWER...

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