Is f(x) = √(x-3)^2+3 a function? How do I know it's a function and its domain and range?

Question

agreene · Answer

$$f(x)=\sqrt{(x-3)^2}+3$$
is that the question? if so... it can be simplified..

agreene · Answer

$$\sqrt{x-3}^2+3$$
$$\cancel{\sqrt{}}x-3\cancel{^2}+3$$
$$x-3+3$$
$$x$$
y=x is a line.

zarkon · Answer

$$\sqrt{f^2}=|f|$$

anonymous · Answer

yes that is the question

zarkon · Answer

$$|x-3|+3$$

anonymous · Answer

why is it an absolute value, how did you get it like that? o.o

zarkon · Answer

if you square a real number it is always non-negative (zero or positive)

when you take the principal value of the square root of a non-negative number you get a non-negative number

anonymous · Answer

yup. What do you mean by the principal value of the square root?

zarkon · Answer

the square root of 4 is $\pm2$
the principal value of the square root of 4 is 2.