Question

find the inverse function of f(x)=ln(2x-3)+2

Answer 1

Step-by-step explanation:

$= > (2x - 3) + 2 \\ = > 2x - 3 + 2 \\ = > 2x - 1 \\ = > 2x = 1 \\ x = \frac{1}{2}$

Answer 2

Concept

Inverse function

In relation to the original function f, the inverse function is represented by $f^{-1}$, and the domain of the original function becomes the domain of the inverse function, and the domain of the given function becomes the domain of the inverse function.

Given

The function of f(x)=ln(2x-3)+2.

Find

We have to find the inverse function.

Solution:

Let y = ln(2x-3)+2

Subtract 2 from both equatity

y-2 = ln(2x-3)

Make exponential on both side

$e^{y-2}= 2x-3$

Add 3 from both equatity

$e^{y-2}+3= 2x$

Divide both sides by 2.

$x=\frac{e^{y-2}}{2} +\frac{3}{2}$.

Hence inverse function is $f^{-1}=\frac{e^{y-2}}{2} +\frac{3}{2}$.