Question

f is a 1-1 function. If f(x) is increasing, is f(inverse)(x) increasing. why

Answer 1

(pseudo) Proof:
Let\[f:A\to B\]be bijective. The inverse function of\[f\]is the function \[f^{-1}\] given by\[f^{-1}=\{(y,x)\in B \times A:(x,y)\in f\}.\]Therefore, if\[f\]is an increasing function, then\[f^{-1}\]is also increasing. QED

Answer 2

you there?

Answer 3

k you lose me with the BxA. isn't that domain and range?