Question

range of a function?

Answer 1

\[y=\sqrt{\ln \frac{ 1 }{ \left| x-2 \right|}}\]

Answer 2

Range is the possible values of y.

\[y = \sqrt{\ln{\frac{ 1 }{ |x - 2| }}} = \sqrt{-\ln{|x-2|}}\]The smallest possible value of y is when sqrt(-ln(|3-2|)) = 0

Small values for |x-2| results in ln producing huge negative numbers, which as |x-2| goes to 0 will tend to infinity.

This give you the range\[y \ge 0, \space y \in \mathbb{R} \]

Answer 3

tend to negative infinity*

Answer 4

Ahh I can look at it like as a limit as x->2. It took me a while but I figured it out. Thank you!

Answer 5

Yeah, exactly!

Yw :)