Question

Arrange the steps in the correct sequence to find the inverse function of %5Cfrac%7B3x-15%7D%7B2%7D%20%20" id="TexFormula1" title=" f(x) = \frac{3x-15}{2} " alt=" f(x) = \frac{3x-15}{2} " align="absmiddle" class="latex-formula">

Answer 1

Answer:

The answer is the attached image

Step-by-step explanation:

In order to determine the inverse of any function, we have to think that the independent variable is "y" instead of "x".

So, firstly we have to free the "x" variable:

$f(x)=\frac{3*x-15}{2} \\f(x)=y\\\\y=\frac{3*x-15}{2}\\ 2*y=3*x-15\\3*x=2*y+15\\x=\frac{2*y+15}{3}$

Then, we have to change the variables to the next form:

$x=f^-^1(x)\\y=x$

Finally, the inverse function is:

$f^-^1(x)=\frac{2*x+15}{3}$

I have attached an image with the sequence of steps:

Answer 2

A useful first step is to swap the variables: put y where x is, and put x where y (or f(x)) is. The rest follows from there.