Why is my answer for Domain and Range incorrect?

Question

For this question, it says to "Find the domain of the following functions using interval notation". 

The answer is boxed, but I was wondering why the answer wasn't "x ≠ 2" since when you plug in 2 it becomes "f(x)=0" which is incorrect. Please clarify for me, thank you

Answer 1

I think you may be confusing domain and range. Take a look at the graph of the quadratic,

f(x) = x² -4x +4 = (x-2)(x-2). It should be clear that the function is defined at all values of x, therefore the domain is (-∞,∞). However the function is not defined when y<0. Therefore the range is [0, ∞).