The function f:R-->R is given by f(x)=4x-3. Solve the equation f[f(x)]-f(1)=0

To solve the equation, we need to determine the term
f(f(x)), that is the result of composition of functions, such as: (fof)(x) =
f(f(x)).

f(f(x)) = 4*f(x) -
3

f(f(x)) = 4*(4x-3) -
3

f(f(x)) = 16x - 12 -
3

f(f(x)) = 16x - 15 (1)

Now,
we'll determine the value of the function at x = 1:

f(1) =
4*1 - 3

f(1) = 1 (2)

We'll
replace (1) and (2) in the equation that has to be
solved:

16x - 15 - 1 = 0

We'll
combine like terms:

16x - 16 =
0

We'll divide by 16 both
sides:

x - 1 = 0

x =
1

The solution of the equation f(f(x)) - f(1)
= 0 is x = 1.