Question

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

Answer 1

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

Answer 2

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

Answer 3

\[\sqrt{f^2}=|f|\]

Answer 4

yes that is the question

Answer 5

\[|x-3|+3\]

Answer 6

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

Answer 7

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

Answer 8

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

Answer 9

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