Give a function f that has an inverse......

Question

tkhunny · Answer

f(x) = x

anonymous · Answer

Give a function f that has an inverse, such that $$domain =  f^{-1}\in \mathbb{R} $$
and that $$Range = f^{-1} \in [-\infty,0)$$

tkhunny · Answer

Aw!  I jumped the gun.

tkhunny · Answer

Do you have a guess?

anonymous · Answer

well I know that the function f has to be $$f \in [\infty,0)$$
and that $$f(x) \in R$$

anonymous · Answer

I just can't think of any restrictions that allow the function to not be able to real with only negative numbers @tkhunny

anonymous · Answer

Woops mistake I mean $$f \in [-\infty,0)$$

tkhunny · Answer

$\infty$ never would have a brace, would it?  Always a parenthesis.

anonymous · Answer

Well I guess but, what kind of function would only work with negative numbers? It can't even include zero so I guess its some kind of reciprocal with an absolute value system or something... than it has to allow all y values to be real..

tkhunny · Answer

How about f(x) = ln(-x)?

anonymous · Answer

can you show me a graph of it so I can visualize it plox?

anonymous · Answer

wouldn't its inverse be $$y = e^{-x}$$

anonymous · Answer

o wait its brilliant excellent  thanks

tkhunny · Answer

:-)  I love it when I just have to sit back and let it soak in.  Good work.

y = ln(-x)

x = ln(-y)

$e^{x} = -y$

$f^{-1}(x) = -e^{x}$ -- Not quite what you suggested.