An inverse function is a function that "reverses" another function: if the function f applied to an input x gives a result of y, then applying its inverse function to y gives the result x, and vice versa, i.e.,
if and only if
.
One of the main properties of function and its inverse function is:
From the diagram you can see that blue and red curves are reflections of each other across the line y = x, then the function h is the inverse, because for every point (x, y) on the graph of f, there is a corresponding point (y, x) on the graph of h.
Answer: correct choice is B.
The graph of a function and its inverse function are symmetric about the line y=x
On the graph above, I made a line y=x using green color.
The function h(x) is the inverse of f(x) because it is symmetric about the line y= x.
Hence option number B is correct.
Thus, The function h is the inverse because for every point (x, y) on the graph of f, there is a corresponding point (y, x) on the graph of h.
Answer:
Remember that a set is a base for some topology on
if satisfy the following properties:
1.
2. For , If
then exist
such that
.
Now, for we verify the above properties:
1. It's clear that
2. Let . Without loss of generality suppose that
. Then
, this implies that
and
and
.
Then, B satisfy the two properties. This show that B is a basis for a topology in