Functions and functions

Algebra Level 3

If f (x) = a+bx and f ( f ( f ( f (x))))= 256x + 425, and if a and b are positive real numbers, then (a-b )=?

The answer is 1.

1 solution

Hemel Sarkar
Aug 30, 2014

f(x)=a+bx or f(f(x))=a+b(a+bx)=a+ab+b^2x like that f ( f ( f ( f (x))))=a+ab+ab^2+ab^3+b^4x=256x+425 so b^4x=256x or b=4. now a+4a+a(4^2)+a(4^3)=425 or 85a=425 or a=5 So a-b=1

Wrong. The value of $b$ is $\pm 4$ . For $b=4$ , we have $a=5$ and for $b=(-4)$ , we have $a=\frac{-25}{3}$ . Both are correct and valid answers. You should edit the problem to say that " $a$ and $b$ are positive real numbers" .

Prasun Biswas - 6 years, 6 months ago

Thanks. I have updated the question accordingly. Great that you noticed that multiple solutions are possible.

Calvin Lin Staff - 6 years, 6 months ago

Functions and functions

The answer is 1.

1 solution

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