Please help me with 1st sum 
1. Let f be an injective function with domain [a, b] and range [c, d]. If  α  is a point in (a, b) such that f has left hand derivative l  and 
right hand derivative r at x = 
α  with both l and r non-zero different and negative, then left hand derivative
right hand derivative of f-1  at x = f( α ) respectively, is 
(A)  1 r , 1 l  (B) r , l  (C)   1 l , 1 r (D) l, r

Dear Student,
Please find below the solution to the asked query:

Letf-1x=gxx=fgx1=f'gx.g'xg'fα=1f'gfαAs x=fαf-1x=αi.e.gx=αg'x=1f'αFor right hand derivate f'α=r and left hand derivative f'α=lHenceg'fα+=1rg'fα-=1l

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