Find the inverse and state if the inverse is a function.

Question

anonymous · Answer

$$\large f(x) = \sqrt[3]{x} − 3 $$

anonymous · Answer

solve 
$$\large x=\sqrt[3]{y}-3$$ for $y$

anonymous · Answer

takes only two steps 
1) add 3
2) cube

anonymous · Answer

$$x^{3}+27 = y?$$

anonymous · Answer

oh no

anonymous · Answer

$$(x+3)^3\neq x^3+27$$

anonymous · Answer

$$x=\sqrt[3]{y}-3\
x+3=\sqrt[3]{y}\
(x+3)^3=y$$ so 
$$f^{-1}(x)=(x+3)^3$$

anonymous · Answer

Ohhhh okay

anonymous · Answer

how you been, haven't seen you in a while?

anonymous · Answer

I've been good. I had a baby back in August so I've been busy with her and my other baby. But I'm relearning stuff before I go back to school next year.

anonymous · Answer

boy or girl?

anonymous · Answer

oh , her, doh

anonymous · Answer

good luck!

anonymous · Answer

Hahaa thanks.
Yeah my first was a boy my second was a girl.
One more question. How do I know if it's a function?

anonymous · Answer

it is a function because , well because it is 
$$g(x)=(x+3)^3$$ is a function, put in a number, get out a number
you would know it was NOT a function if you had say a $\pm$ in it
like if you solve 
$$x=y^2$$ for $y$ you would have to say 
$$y=\pm\sqrt{x}$$ and that is NOT a function

anonymous · Answer

Oh yeah! Sorry it's been a while in this class.