http://www.wolframalpha.com/input/?i=f%28x%29%3D7x%5E9+inverse Is the inverse or blue lines a function or is 0 a common y input?

Question

anonymous · Answer

red - original, blue -inverse. It's in the lower left corner of the graph

anonymous · Answer

So if we are just considering the lower left corner it would be a function

anonymous · Answer

sorry I meant lower right corner just for labels of graphs. Yes, inverse is a function

anonymous · Answer

Ok and the inverse can also be written as (x/7)^9?

anonymous · Answer

(x/7)^(1/9)

anonymous · Answer

but why is it 1/9? is that the complete inverse?

whpalmer4 · Answer

You had $$f(x) = y=x^9$$swap variables and solve for y to get the inverse
$$x = y^9$$$$x^{1/9} = y = f^{-1}(x)$$

whpalmer4 · Answer

Don't be confused the by -1 in $f^{-1}(x)$, there's only one function for which $$f^{-1}(x) = \frac{1}{f(x)}$$

and it isn't $$y = x^9$$ :-)

anonymous · Answer

If U will do f(f^(-1)(x)) it will be equal x. sorry for strange notation