Final answer:
The value of x for which f(f(x)) equals f(x), given f(x) = 2x - 3, is x = 3, obtained by first substituting f(x) into itself and then solving for x.
Step-by-step explanation:
To solve for the values of x such that f(f(x)) = f(x), where f(x) = 2x - 3, we first find f(f(x)).
f(f(x)) is calculated by substituting f(x) back into itself:
f(f(x)) = 2(2x - 3) - 3
Which simplifies to:
4x - 9
Setting f(f(x)) equal to f(x) gives us:
4x - 9 = 2x - 3
Rearranging and solving for x results in:
2x = 6
x = 3
So, the value of x for which f(f(x)) = f(x) is x = 3.