SOLUTION: I need help in this coordinate graph. It says draw the graph of the inverse of f(x)=-3/2x-3 on a coordinate grid.

Algebra ->  Coordinate-system -> SOLUTION: I need help in this coordinate graph. It says draw the graph of the inverse of f(x)=-3/2x-3 on a coordinate grid.      Log On


   

Question 960733: I need help in this coordinate graph. It says draw the graph of the inverse of f(x)=-3/2x-3 on a coordinate grid.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i believe you mean the inverse graph of f(x) = -3 / (2x-3)

set y = f(x) to get:

y = -3 / (2x-3)

swap y with x to get:

x = -3 / (2y-3)

now you need to solve for y.

multiply both sides of the equation by (2y-3) and divide both sides of the equation by x to get:

2y-3 = -3/x

add 3 to both sides of the equation to get:

2y = 3 - 3/x

divide both sides of the equation by 2 to get:

y = (3 - 3x) / 2

that should be your inverse equation.

if so, then its graph should be a reflection of the original equation of y = -3(2x-3)

your original equation is y = -3 / (2x-3)

your inverse equation is y = (-3/x + 3) / 2

the grpah of your equations is shown below:

$$$

red is your original equation and blue is your inverse equation.

those equations are reflections about the line y = x.

when the equations are inverse, the f(x,y) = g(y,x), where f and g are inverse equations of each other.

in the graph, that can be seen by the intersections of the lines y = -x+10 and y = -x + 5 with the respective graphs of the equations that are inverse to each other.

look for the red graph on one side of y = x and the corresponding point of the blue graph on the other side of y = x.