INVERSE FUNCTION

inverse function

In this post we define inverse function and also provide an example to clear the concept of it.

The inverse function of f denoted by f-1 is a function from Y onto X and is defined by x= f–1(y)  for all x in y if and only if as y=f(x) , for all x

The set X of all possible input values is known as domain and the set of all values  of f(x) as x varies through X is called range  of a function.

inverse function

Example: Let f : R → R be the function defined as f(x)= 2x+1 then find -1(x)

Solution.

                             As    f(x) = 2x+1

                                     y – 1 = 2 x 

                                    x=\frac{y - 1}{2}           → (1)

we know that   f( x ) = y   

                          x = -1(y)

By putting value of x in (1) we get

                            f^{-1}\left ( y \right )=\frac{y-1}{2}

 

By Replacing y = x we get

                          f^{-1}\left ( x \right )=\frac{x-1}{2}

                        

 

 

For other Definitions Click here

 

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