Question

One-one,many one,onto,into?

Answer 1

\[\LARGE f:R \rightarrow R ~and ~f(x)=\frac{e^{|x|}-e^{-x}}{e^x+e^{-x}}\]

Answer 2

have you graphed it?

Answer 3

I broke this into 2 parts..
\[f(x)= \frac{e^x-e^{-x}}{e^x+e^{-x}}~if~x>=0\]
\[f(x)= \frac{e^{-x}-e^{-x}}{e^x+e^{-x}}~if~x>=0\]
I don't know how to graph it.

Answer 4

sorry its x<=0 in 2nd one*

Answer 5

I'm taking the wrong LCM after this won't it be e^x^2?

Answer 6

https://www.desmos.com/calculator
just type y=(your equation)

Answer 7

how do i input a fraction? and BTW i don't want to solve it by graph.I want to know what will we get after taking the LCM.

Answer 8

\[\LARGE e^{x}+\frac{1}{e^x}=?\]

Answer 9

won't it be
\[\LARGE \frac{e^{x^2}+1}{e^x}\]

Answer 10

Hey if u take LCM in 1st eqn (the one u get by breaking in parts), u get:\[\frac{ e ^{x ^{2}} - 1 }{ e ^{x ^{2}} + 1 } \]
And u get zero for second part...
So it is Many one(coz for all x>=0 we get 0) and Onto(coz x belongs to Real Nos.)

Answer 11

Why is desmo's graph like this then?
http://prntscr.com/12y5qc
it is forever increasing..

Answer 12

sorry x<=0 in second part

Answer 13

my solution says after taking LCM that it's..
\[\LARGE \frac{e^{2x}-1}{e^{2x}+1}\]

Answer 14

so isnt my answer correct (even acc. to the graph)

Answer 15

Thats wt i said @DLS

Answer 16

forever increasing functions are one-one because a value can't be repeated

Answer 17

u wrote e to the power x squared
and its
e to the power 2x :|

Answer 18

WF says too that its e to the power 2x :o

Answer 19

oooooohhh yeah sorry!!!!!!!

Answer 20

how is it 2x!!

Answer 21

(e^x) * (e^x) = e^2x [base are same powers are added]

Answer 22

oh :P i see

Answer 23

But the answer still remains same!!!!!!

Answer 24

Well its many one into..

Answer 25

No its onto only

Answer 26

since codomain is not equal to range :|

Answer 27

codomain is R and range is only +ve numbers

Answer 28

didn't we prove just now that all negative values will get attached to 0 :o

Answer 29

so on this base we can say all negative values are getting attached to 0 so many one and into

Answer 30

Range = codomain is a condition for surjective funx(one one and onto both)

Answer 31

but range is not equal to codomaain