Finding the Inverse of a Cubic Polynomial

[QuarkCharmer]

Homework Statement

Find the inverse of the function.

f(x)=2x^{3}+5

Homework Equations

Possibly the quadratic equation.

The Attempt at a Solution

f(x)=2x^{3}+5

y=2x^{3}+5

-2x^{3}=-y+5

x^{3}= \frac{-y+5}{-2}

x= \pm\sqrt[3]{\frac{-y+5}{-2}}

y= \pm\sqrt[3]{\frac{-x+5}{-2}}So the solution is two inverse functions? like..f^{-1}(x)= \sqrt[3]{\frac{(-x+5)}{-2}}

and

f^{-1}(x)= -\sqrt[3]{\frac{(-x+5)}{-2}}

I'm not sure that is what the professor is looking for? Thank you.

 

[Mentallic]

You're confusing x^2=1 \to x=\pm 1 with x^3=1 \to x=1

x=-1 does not satisfy x^3=1

 

[QuarkCharmer]

Ah, yes it seems I am.

The inverse function is simply:

f^{-1}(x)= \sqrt[3]{\frac{(-x+5)}{-2}}

then?

 

[aim1732]

Since the function is monotonic increasing function it has only one inverse and you have it.

 

[QuarkCharmer]

So the correct inverse function for

f(x)=2x^{3}+5

is

f^{-1}(x)= \sqrt[3]{\frac{(-x+5)}{-2}}
?
Thanks!

 

[Mark44]

Yes, but that's the same as
f^{-1}(x)= \sqrt[3]{\frac{x-5}{2}}

 

[QuarkCharmer]

Yes, but that's the same as
f^{-1}(x)= \sqrt[3]{\frac{x-5}{2}}

Right!

Thanks a lot for the help. This just sort of showed up on a worksheet, and we have not covered inverse functions yet, I had to read ahead in the book to even get the slightest idea.

It's very much appreciated!