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

The degree of the differential equation d2ydx2+3[dydx]2=x2log[d2ydx2] is 

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