College Algebra help please!

This is for review for my final exam. I would like to learn how to grasp the concept and answer the problem correctly, so please explain each step.

Find the inverse of the following function:

f(x) = 7 over (or divided by) 2x-3

Thank you in advance! Will choose best answer!

hi,

to find an inverse function, simply replace the x with a y, and solve for y.
f(x) = 7/(2x-3)
replacing the x with y, and vice versa, we have:
x=7/(2y-3)
x(2y-3)=7
2xy-3x=7
2xy=7+3x

y= (3x+7)/(2x)

if you graph both of these functions, you will see that the inverse is a reflection of the original function over the line y=x :)

good luck on your final!

y = 7/(2x - 3)

Solve for x in terms of y:

2xy - 3y = 7

x = (7 + 3y)/(2y)

Switch the variables:

f^-1(x) = (7 + 3x)/(2x) = 7/(2x) + 3/2