INVERSE FUNCTIONS (MATH) HAVE NO IDEA HOW TO DO THIS.....10 pts!!! :)?

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

Let's call this f(x).

f(x) = (2/3)x - 4

The way to find the inverse of a function is to first make f(x) into y.

y = (2/3)x - 4

Now, swap the x and y variables.

x = (2/3)y - 4

and solve for y.  The result will be your functional inverse.

x + 4 = (2/3)y

Multiply both sides by (3/2), to get

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

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

(3/2)x + 6 = y

Therefore,

y = (3/2)x + 6

Make your concluding statement.

f^(-1)(x) = (3/2)x + 6

Answer 2

Like they say: switch variables and solve for the "new" y.

x = (2/3)y - 4

x + 4 = (2/3)y

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

y = (3/2)x + 6

So the inverse of the original function is y = (3/2)x + 6

Answer 3

Okay, we'll use their method.  We'll switch variables and then solve for the new y.  If

y = (2/3)x - 4, then we go ahead and switch:

x = (2/3)y - 4, and so we solve for y:

x + 4 = (2/3)y

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

y = (3/2)x + 6

Let's test this.  If we take the initial function, x maps from x to

(2/3)x - 4

We then put (2/3)x - 4 into the "x" value for our inverse function:

y = (3/2)((2/3)x - 4) + 6, so:

y = x - 6 + 6 = x.  

So then this checks out: y = (3/2)x + 6 is the inverse function for y = (2/3)x - 4.