Question

Ho do I explain f(x)=x^3 as a function that has an inverse? I'm not sure what to do here.

Answer 1

\[\large g(y)=y^{\frac{1}{3}}\]

Answer 2

Okay thank you so much!

Answer 3

u c wut i did there?

Answer 4

Important thing about x^3 is that it is non-decreasing. This is a big deal.

Answer 5

okay so you switch the x and y values and then times by 3 to get y by it self right?

Answer 6

I would talk a lot about that if you have to write about it. y^(1/3) is also non-decreasing. If your function doubles-back on itself, then you have to start tweaking the domain and range.

Answer 7

No. What I did was like this:
\[y=f(x)=x^3\]Suppose f has an inverse of the form:\[x=g(y)=y^a\]Then\[y^a=(f(x))^a=(x^3)^a=x^{3*a}=x\]\[3*a=1\]\[a=\frac{1}{3}\]