Question

Find two functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] does not equal x

Answer 1

I wouldn't even know where to begin here.

Answer 2

@whpalmer4

Answer 3

@bahrom7893

Answer 4

@inkyvoyd

Answer 5

@amistre64

Answer 6

@Luigi0210

Answer 7

I guess we should try to avoid using simple linear functions.
A composition of linear functions will always give us g(f(x))=x if it already gave us f(g(x))=x.

So we need something a little bit fancier.
Like a function that is `not one-to-one`.

Answer 8

I tried arctan and tan, but she (my teacher) said they'd both come to x.

Wolfram alpha says she's wrong though?

Answer 9

Hmm, ya seems like she's wrong >.<
I have another idea.. how bout these two functions :)

Answer 10

\[\large\rm f(x)=x^2,\qquad\qquad\qquad g(x)=\sqrt{x}\]

Answer 11

Those both equal x

Answer 12

\[\large\rm g(f(x))=\sqrt{x^2}=|x|\]

Answer 13

Ah, nevermind

I just saw that

Answer 14

\[\large\rm f(g(x))=\sqrt{x}^2=x\]When the square is on the outside we have something else going on like we see here :)

Answer 15

But it's happening because x^2 is not one-to-one.
Seems like tangent should give you some similar shenanigans, but i dunno >.<

Answer 16

Yeah...

Thank you! You've helped bunches1

Answer 17

*!

Answer 18

cool c: