Find f(-1) (inverse) if y=4x+2/3x-1 and x is not equal with 1/3

Before we find , let's think for a minute about what  does, and what it means to find the inverse of a function. A function  essentially takes a value  from the domain and maps it to another value  in that function's range according to a set of rules. Here, those rules are defined by the formula



All the inverse does is swap the domain and range of the function. Now, instead of trying to map  to , we're trying to find a set of rules that'll map  back to . To find those rules, all we have to do is solve the above equation for .

First, we'll multiply both sides of the equation by  to get it out of the denominator:



Cancelling on the right side and distributing on the left, we get:



Next, we collect all of our x terms on one side, and all of our non-x terms on the other:



Let's rearrange the right side and factor out an x on the left:



And finally, we divide both sides by  to obtain our



This equation gives us the "rules" for mapping any given y in the range back to an x in the domain. If we swap the domain and the range, we can define our function 

2x^2 -2x -12 = 02(x -3)(x +2) = 0see below for explanation

step-by-step explanation:

equation

you are asked to write the equation

  expression = 0

using the given expression. when you do that, you have

  2x^2-2x-12 = 0

factoring

you can see that each of the coefficients is even, so a factor of 2 can be removed immediately.

  2(x^2 -x -6) = 0

if you multiply the binomials (x+a)(x+b), you get

  (x +a)(x +b) = x^2 +(a+b)x +ab

this tells you the coefficient of x is the sum of two factors of the constant term. here, that means -1 is the sum of two factors of -6. we want to know those factors so we can factor the trinomial.

  -6 = -1×6 = -2×3 = -3×2 = -6×1

the factor pair that sums to -1 is {-3, 2}, so our factorization is

  2(x -3)(x +2) = 0

solutions

the solutions to this equation are the values of x that make the product zero. a product is zero only when only of the factors of the product is zero. here, that means

  x - 3 = 0

  x = 3 . . . add 3 to both sides of the equation

or

  x +2 = 0

  x = -2 . . . add -2 to both sides of the equation

the solutions to the equation are x=3 or x=-2. both of these values of x satisfy the equation—they make it be true.

It creates dogx^2 and then flip your answer and multiply by 2