# 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.

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

Solution.

As    f(x) = 2x+1

y – 1 = 2 x

$x=\frac{y&space;-&space;1}{2}$           → (1)

we know that   f( x ) = y

### x = f -1(y)

By putting value of x in (1) we get

$f^{-1}\left&space;(&space;y&space;\right&space;)=\frac{y-1}{2}$

By Replacing y = x we get

$f^{-1}\left&space;(&space;x&space;\right&space;)=\frac{x-1}{2}$