Inverse Function Formula

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 =

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

 

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