Thread: Need to find Inverse of...

1. Need to find Inverse of...

Can anyone help me out for finding the inverse of this function? I'm not quite sure how to find the inverse of a polynomial...

$y=2x^3+3x^2+7x+4$

Thank you!

Also if you can help me find this integral...

$
\int_0^{\frac{\pi}{4}}\tan^2{x} dx
$

2. Originally Posted by yamuda
Can anyone help me out for finding the inverse of this function? I'm not quite sure how to find the inverse of a polynomial...

$y=2x^3+3x^2+7x+4$

Thank you!

Also if you can help me find this integral...

$
\int_0^{\frac{\pi}{4}}\tan^2{x} dx
$
For the first one swith x's and y's and solve for y again.

second one $\int_0^{\frac{\pi}{4}}tan^2(x)dx=\int_0^{\frac{\pi }{4}}[sec^2(x)-1]dx=tan(x)-x\bigg|_0^{\frac{\pi}{4}}=1-\frac{1}{4}\pi$

3. Originally Posted by Mathstud28
For the first one swith x's and y's and solve for y again.

second one $\int_0^{\frac{\pi}{4}}tan^2(x)dx=\int_0^{\frac{\pi }{4}}[sec^2(x)-1]dx=tan(x)-x\bigg|_0^{\frac{\pi}{4}}=1-\frac{1}{4}\pi$
mmm thanks a lot, but im having trouble with the inverse, i know how to do inverse, but im not sure what to do with this polynomial....

4. Originally Posted by yamuda
Can anyone help me out for finding the inverse of this function? I'm not quite sure how to find the inverse of a polynomial...

$y=2x^3+3x^2+7x+4$

Thank you!
[snip]
Unless you can write it in the form $y = a(x - h)^3 + k$ (which you can't - there's a point of inflexion at (-1/2, 1) but it's not a stationary point of inflexion) you'll have to solve $x = 2y^3 + 3y^2 + 7y + 4$ for y using Cardano's method (see Cubic function - Wikipedia, the free encyclopedia)