- #1

srfriggen

- 307

- 7

I've written it as x=2y^3+3y+2 and am trying to solve for y, but I can't seem to factor anything out correctly.

Anyone see how this can be solved?

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In summary, The inverse of a function is the function that undoes the original function, which can be found by replacing f(x) with y, swapping the x and y variables, solving for y, and replacing y with f^-1(x). To factor a polynomial, we can use the rational root theorem to find the possible rational roots and then use synthetic division to get the factored form. The simplified form of a function can be found by factoring out a common term and rearranging the terms. To solve for x in the inverse function, we can use algebraic manipulation. The inverse function can be graphed by plotting the points (x,y) and reflecting them over the line y=x.

- #1

srfriggen

- 307

- 7

I've written it as x=2y^3+3y+2 and am trying to solve for y, but I can't seem to factor anything out correctly.

Anyone see how this can be solved?

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- #2

QuarkCharmer

- 1,051

- 3

https://www.physicsforums.com/showthread.php?t=47117

Is this a pre-calc problem?

- #3

srfriggen

- 307

- 7

It's a problem I just came up with and tried to solve :/

The inverse of a function is the function that undoes the original function. In this case, we need to solve for x in terms of y. To do this, we can follow the steps of finding the inverse:

1. Replace f(x) with y

2. Swap the x and y variables

3. Solve for y

4. Replace y with f^-1(x)

Therefore, the inverse of f(x)=2x^3+3x+2 is f^-1(x)=(y-3)/(2y^3+2).

To factor a polynomial, we need to find its roots or zeros. We can use the rational root theorem to find the possible rational roots of the polynomial. In this case, the possible rational roots are ±1 and ±2. After plugging in these values into the function, we find that x=1 is a root. Using synthetic division, we get the factored form of f(x)=(x-1)(2x^2+2x+2).

To simplify the function, we can factor out a 2 from each term, giving us f(x)=2(x^3+1.5x+1). We can then rearrange the terms to get f(x)=2(x^3+1.5x+1)=2((x^3+1)+(0.5x+1))=2((x+1)(x^2-x+1)+(0.5(x+1)))=2(x+1)(x^2-x+1.5).

To solve for x in the inverse function, we can follow the steps of finding the inverse:

1. Replace f(x) with y

2. Swap the x and y variables

3. Solve for y

4. Replace y with f^-1(x)

In this case, we can use algebraic manipulation to isolate x in terms of y.

Yes, we can graph the inverse function by plotting the points (x,y) where x is the input and y is the output. This will give us a reflection of the original function over the line y=x. We can also use the graphing calculator to plot the inverse function and verify that it is indeed the inverse of the original function.

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