Question

How does one find the inverse function of f(x)= le="\frac{1}{3x-1}" alt="\frac{1}{3x-1}" align="absmiddle" class="latex-formula">

Answer 1

Answer:

$\displaystyle f^{-1}(x)=\frac{1+x}{3x}$

Step-by-step explanation:

The Inverse of a Function

The procedure to find the inverse of the function is:

* Write the function as a two-variable equation:

$\displaystyle y=\frac{1}{3x-1}$

* Solve the equation for x.

Multiply by 3x-1

$y(3x-1)=1$

Divide by y:

$\displaystyle 3x-1=\frac{1}{y}$

Sum 1:

$\displaystyle 3x=\frac{1}{y}+1$

Operate the right side:

$\displaystyle 3x=\frac{1+y}{y}$

Divide by 3:

$\displaystyle x=\frac{1+y}{3y}$

* Swap the variables:

$\displaystyle y=\frac{1+x}{3x}$

Write back into function form:

$\boxed{\displaystyle f^{-1}(x)=\frac{1+x}{3x}}$