Question

Determine the equation of the inverse of y=2^3x-1

Answer 1

Answer:

f^-1(y) =[ In(x-2) + 1] /3

Step-by-step explanation:

The inverse of this expression is to find x

Now taking In of both sides we have

y=2^3x-1

In y = In2^3x-1

In y = (3x- 1)In 2

(Iny / In2) + 1= 3x

x =[ (Iny / In2) + 1] /3

Therefore the inverse of y is

f^-1(y) =[ (Inx / In2) + 1] /3

f^-1(y) =[ In(x-2) + 1] /3

Answer 2

The equation of the inverse of the provided equation, which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

What is the inverse of an equation?

The inverse of an equation is the reverse of the original equation. The equation and the inverse of it has symmetry in each other.

To find the inverse of equation, we have to interchange the variable of equation to each other.

The given equation is,

$y=2^{3x-1}$

Taking log both side of the equation,

$\ln y = \ln 2^{3x-1}$

Use the log of power and simplify the equation further, as,

$\ln y = \ln 2^{3x-1}\\\ln y = (3x-1)\ln 2\\\dfrac{\ln y}{\ln 2} = (3x-1)\\\ln (y-2)= (3x-1)\\\ln (y-2)+1= 3x\\x=\dfrac{\ln (y-2)+1}{3}$

Interchange the place of x and y,

$y=\dfrac{\ln (x-2)+1}{3}$

This is the required inverse equation.

Thus, the equation of the inverse of the provided equation which is equal to the reverse of the original equation, is y=(ln(x-2)+1)/3.

Learn more about the inverse of an equation here;

https://brainly.com/question/5219726

#SPJ2