Suppose that f(x) = ax + b, where a and b are real numbers.

Suppose that f(x) = ax + b, where a and b are real numbers. Given that
f(f(f(x))) = 8x + 21, what is the value of a and b?

Steps please

a(a(ax + b) + b) + b = 8x + 21

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

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

a^3x = 8x

a = 2

(a^2)b + ab + b = 21

4b + 2b + b = 21

7b = 21

b = 3

Simply calculate
f(f(f(x)))=f(f(ax+b))
=f(a^2x+ab+b)=a^3x+a^2b+ab+b

Hence in this case, a^3=8 so a=2, so 4b+2b+b=7b=21 hence b=21/7=3.