Tagged Questions
3
votes
1answer
60 views
Why $ g(p) = 0.5 p^{-0.2} + 0.5 p^{-0.5} $ has a well-defined inverse that is continuous and strictly decreasing.
A book that I am reading claims the following about the function $ g(p) = 0.5 p^{-0.2} + 0.5 p^{-0.5} $ (which is a demand function):
Formal arguments based on the Intermediate Value Theorem and ...
0
votes
1answer
57 views
Relationship between real inverses of analytic functions
Take some analytic function, $f(x)$, that goes from $-\infty$ to $\infty$, with a finite number of points such that $\frac{df}{dx}=0$. You can divide the y axis into intervals, where the boundary ...
2
votes
2answers
126 views
$f(x,y)$ in polar coordinates
So, I have $ f(x,y) = (x^2-y^2, 2xy) $,
which is a local $\mathcal C^1$ isomorphism in $\mathbb R^2 \setminus \{(0,0)\}$.
I have to write this function in polar coordinates:
$$f(x,y) = ...
