Question

Can anyone explain the step by step solution for this question?

Answer 1

http://i.imgur.com/6YKFaOB.png

Answer 2

Here is the solution,
http://img23.imageshack.us/img23/8403/l19m.png
http://i.imgur.com/ZTz9oUC.png

Answer 3

@hartnn @ganeshie8

Answer 4

?? which part ?

Answer 5

From it is clear...:P

Answer 6

dint get u.... it is clear nw ? :)

Answer 7

i mean from the part where it says
It is clear that f:[1,-1]->Range f is onto !

Answer 8

onto means, all the elements in Range have some preimage.
here, there are no discontinuities, so all output values have some input value

wats big deal ?

Answer 9

i know what onto means but how did we figure it out heeree

Answer 10

i see
they mean f:[-1, 1] --> R

they mean Real numbers here right ?

Answer 11

seems so

Answer 12

that means (inf, inf) is the Range
then its definitely NOT onto, cuz inputs in [-1, 1] will not output all Real numbers

Answer 13

looks the work is incorrect to me

Answer 14

wahi to :/

Answer 15

but the statement in the solution makes sense

Answer 16

it says,
It is clear that f:[1,-1]->Range f is onto !


it doesnt say
It is clear that f:[1,-1]->R is onto !

Answer 17

confusing :/

Answer 18

okay work this wid somebody else... i have same questions as u on this ..

Answer 19

kal exam hai :/ no one else online..duh ! @hartnn again...

Answer 20

okay, here is the thing :-
look at how they defined the inverse function DOMAIN :-
g: Range f -> [-1, 1]

Answer 21

read the quesiton also again, they want inverse funciton wid in the Range of f oly.

f is is onto in that range, cuz its not discontinous in that range.

Answer 22

does that make sense ?
i am at peace wid the solution now. it makes perfect sense to me

Answer 23

didnt get it :/

Answer 24

f is defined in [-1, 1]

Answer 25

its inverse is defined JUST in the range of f

Answer 26

within the range of f, f is onto. <<-- if u agree wid this, we can find inverse within this range

Answer 27

okay..

Answer 28

f is not onto, when its range is R.

if u agree that f is onto, when Range is restricted, to watever values it outputs.
when u can go ahead and find its inverse g in that restricted range.
g: Range of f ->[-1, 1]

Answer 29

something still confusing u ?

Answer 30

not yet thankfully !

Answer 31

we know f is onto between [-1, 1], when restricted its Range, simply by observing that f is not discontinous in that domain