Given fofof=64x-21,find f(x)
let f(x) = ax + b
then
f(f(x)) = a(ax+b) + b
= a^2 x + ab + b
so a^2 = 64 ---> a = ±8
then ab+b=-21
b = -21/(a+1)
if a=8 , b = -21/9 = -7/3
if a = -8, b = -21/-7 = 3
f(x) = 8x - 7/3 OR f(x) = -8x + 3
check:
if f(x) = -8x + 3
f(f(x)) = -8(-8x+3) + 3 = 64x - 21
if f(x) = 8x - 7/3
f(f(x)) = 8(8x - 7/3) - 7/3
= 64x - 56/3 - 7/3
= 64x - 21
both equations are valid.
To find f(x) from the given equation fofof = 64x - 21, we need to understand the notation used.
The notation fofof represents the composition of the function f with itself, which means that we need to substitute fofof in terms of x back into the original equation.
Let's start by substituting fofof with f(x) in the equation:
f(x) = 64x - 21
Now we have the expression for f(x).