Please send the solution to the problem given in the attachment

doubt

inverse calculate karne k liye variables change kar sakte hai.

agar ni karna chaho to bhi koi problem ni hai. bas last me f-(x) = function of x , me hi likhna.

what type of inverse is that?

Here I have taken Domain=R to codomain R

if we take domain N (natural no.) and codomain R then inverse not exist

but for inverse only one one condition is sufficient

no , its absolutely incorrect .

there may be some restrictions here ..

Alka ma'am sent me

There may be some restrictions . Ask her to send complete image and then read..

so acc . to you if bijective then inverse exists, right?

yes , see my above counter example .

you say this is absolutely incorrect....ok.... could you plz tell me correct definition of inverse/invertible function

and remember not give any example ....only definition

and one more thing....you say there is some restrictions....so also tell about that restrictions

see , from class 12 NCERT book

if your definition is correct then disprove my above counter example .

you have send , then you will tell restrictions .. send me link from where you found this ... I will check ..

see your NCERT above statement also what they say....if there exist a function g such that gof and fog are identity function

most correct definition of inverse function is this....

your counter example answer

see it's definition in any standard differential calculus book not in NCERT

my definition is for codomain . Your definition is restricted to range . If we restrict codomain to range then we can absolutely say that inverse function exist for restricted function . But what about codomain ?

conclusion is that , 1-1 , onto condition is necessary for function to be invertible . (from your definition also )