WHAT IS THE INVARIENT FOR THIS AND HOW DO YOU SOLVE? 10 points.... :) (math)?

Question

Says:

Determine the inverse functions for the functions below. Begin by switching varaiables in the original function, then solving for the 'new' y. For each case sketch the function and its inverse.

Have no idea what this is or what to do. Please explain how u found answer. 10 Points! :)

3. y= (2/3)x - 4

Answer 1

hey,

The inverse is a function that pretty much kills the original function. So for y=(2/3)x - 4

you start by switching x and y so you have

x=(2/3)y-4 and now you solve for y

so you have

x+4=(2/3)y

y= (3/2)(x+4)

and that function is the inverse function

hope this helps

Answer 2

y = (2/3)x -4   switch places with x and y

x = (2/3)y -4   solve for y.  First add 4 to both sides

x + 4 = 2/3y   multiply both sides by 3

3x + 12 = 2y   divide both sides by 2

3/2x + 6 = y  

y = 3/2x + 6   this is the inverse function

Now graph both lines.  The first on you plot -4 on the y-axis then go up 2 and right 3 and draw the line.

For the second line plot 6 on the y-axis then go up 3 and right 2 and draw the line.

Answer 3

Solving for x:

y = 2/3x - 4

2/3x = y + 4

x = 3/2(y + 4)

x = 3/2y + 6

Answer: x = 3/2y + 6

Proof:

y = 2/3(3/2y + 6) - 4

y = y + 4 - 4

y = y

Answer 4

y= (2/3)x - 4

y+4 = (2/3)x

(3/2)(y+4) = x

Hence etc

Is that difficult? What invarient are u looking for? or you want to say inverse?

Answer 5

No idea bro.

But if I were to guess, I would just flip the slope

For example,

y = (3/2)x - 4

Answer 6

y = 2/3x - 4

2/3x = y + 4

x = (y + 4) 3

         2

y = (x + 4)3/2

i think thats how u do it