determine the inverse function of   `f(x) = sqrt(x + 3)` state the domain and range for its function & its inverse and sketch the graph of both the function and inverse 



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Posted on (Answer #1)

Let g  be the inverse function of f ,then by def. of inverse



`g(f(x))=x`    (i)



`g(f(x))=g(y)=x`     (i)




`x=y^2-3`         (ii)

from (i) and (ii)



inverse of f(x) is g(x) where



domain of f=`{x :x>=-3 ,x inR}`

range of f=`{ x : x>=0 , x in R}`

domain of g =`{x : x>=0 ,x in R}`

range of g= { x  , x greater or equal to -3 ,x is real no. }

Graph in red for the function f(x).

and green for the function  g(x).


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