Final answer:
The limit as x approaches 3 of the given function is 4.
Step-by-step explanation:
To find the limit as x approaches 3 of the function f(x), we first need to evaluate the function at x = 3. Since the function is given as a range, we need to find the values of f(x) that satisfy the given inequality for x ≥ 0.
Plug in x = 3 into both sides of the inequality and evaluate:
3(3) - 5 ≤ f(3) ≤ 3^2 - 3(3) + 4
9 - 5 ≤ f(3) ≤ 9 - 9 + 4
4 ≤ f(3) ≤ 4
Since f(3) is always equal to 4, the limit as x approaches 3 of f(x) is also equal to 4.