# Inverse Function Formula

In mathematics, the inverse function is a function that reverses the other function. For instance, the function

$$\begin{array}{l}f(x)=y\end{array}$$
, then the inverse of
$$\begin{array}{l}y\end{array}$$
is
$$\begin{array}{l}g(y)=x\end{array}$$
. If a function has an inverse function, it can be termed as invertible.

Let

$$\begin{array}{l}f\end{array}$$
be the function and the inverse be f-1.  It can also be written as
$$\begin{array}{l}g(f(x))=x\end{array}$$
. The formula for inverse function is,

$\large f(x)=y\Leftrightarrow f^{-1}(y)=x$

### Solved Examples

Question 1: Find out the inverse function of f(x) = 2x + 3 ?

Solution:

Given function is,
f(x) = y = 2x + 3

Inverse function equation is, f-1(y) = x

So

$$\begin{array}{l}x\end{array}$$
can be find out from the above expression.

2x = y – 3

$$\begin{array}{l}x=\frac{y-3}{2}\end{array}$$

So, f-1 =

$$\begin{array}{l}\frac{y-3}{2}\end{array}$$