f(x) and g(x)

[danmc]

In need to idnetify the functions f(x) and g(x) where f(g(x)) = x, but g(f(x)) does not equal x. Have tried for a few days without any luck. can anyone help?

 

[lookagain]

In need to [identify] the functions f(x) and g(x) where f(g(x)) = x, but g(f(x)) does not equal x.

danmc,

do you know about (sqrt{x})^2 = x, but that sqrt{x^2} = |x|, which is not equal to x ** ?






** Not for negative values of x, anyway.

 

[danmc]

thank you for your reply. I do know and understand what you said, but i need to provide two functions (f(x) and g(x)) that when you take f(g(x) you get x, but when you take g(f(x) you do not get x. thanks again.

 

[lookagain]

thank you for your reply.
I do know and understand what you said, > > > but i need < < <
to provide two functions (f(x) and g(x)) that when
you take f(g(x) you get x, but when you take g(f(x) you do not get x.
thanks again.

I gave you all of the information to do it.

I'll be more direct.

Let \(\displaystyle f(x) \ = \ x^2\)


And have \(\displaystyle g(x) \ = \ \sqrt{x}.\)


Now, work out f(g(x)) and g(f(x)).

 

[danmc]

Thanks. I actually figured this out yesterday after re-reading your post, but it is nice to be able to check my work. Thanks again