# Inverse Function Formula

In mathematics, the inverse function is a function that reverses the other function. For instance, the function  $f(x)=y$, then the inverse of $y$ is $g(y)=x$. If a function has an inverse function, it can be termed as invertible.

Let $f$ be the function and the inverse be f-1.  It can also be written as $g(f(x))=x$. 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 $x$ can be find out from the above expression.

2x = y – 3

$x=\frac{y-3}{2}$

So, f-1 = $\frac{y-3}{2}$

#### Practise This Question

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm The diameter of the circle with centre O’ is 10cm. What is the length of the tangent PC?