Inverse Function - Chapter 4 Algebra | Optional Mathematics
Chapter-4| Inverse Functions| Class-10
Inverse Function
The reverse of a given bijective function is known as inverse function.
Keeping (-1) as the power of the given function denotes the inverse of
that function. Eg: $f^{-1}$
A bijective function is a one to one (injective) onto (surjective)
function.
In other words, the function that we obtain after interchanging the domain
and range, is said to be inverse function.
Let us have a function: f= {(1,2),(2,3),(3,4)}
Domain of the above function = {1,2,3}
Range of the above function = {2,3,4}
Now, when we want the inverse function of 'f' i.e. $f^{-1}$ we interchange
the position of domain and range in the function.
So, we obtain, $f^{-1}$ = {(2,1),(3,2),(4,3)}
Domain of the inverse function = {2,3,4}
Range of the inverse function = {1,2,3}
So, when we obtain an inverse function, the domain of the previous
function becomes the range and the range of the previous function becomes
the domain of the inverse function.
Remember: Not every inverse function of a function is necessarily
a function.
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