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  • Let f(x)=(x+1)^2 , where x>= -1. if g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y=x , then g(x) equals

Let f(x)=(x+1)^2 , where x>= -1. if g(x) is the function whose graph is the reflection of the graph of f(x) with respect to the line y=x , then g(x) equals

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Solution:  The sought for function  g(x) is nothing but the inverse

                 of the given function  f(x).

                Now ,    x=sqrty-1    or    f^-1(y)=sqrty-1

             or    f^-1(x)=sqrtx-1, which is well defined for xgeq 0.

             Moreover ,   f  is  one-one and onto.

               

Posted by

Deependra Verma

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