What property of a continuous invertible function is obviuos from its graph?

Question

What property of a continuous invertible function is obviuos from its graph?

Answer 1

It never crosses the y=0 line.

Answer 2

a.) the two graphs ought to constantly bypass. we are in a position to state this situation as given 2 applications f and g non-end over the era [0,one million] such that h(0) < g(0) and h(one million) > g(one million), then there exists a factor c interior the era (0,one million) such that h(c) = g(c) b.) enable f(x) = g(x) - h(x). because of the fact that g and h are non-end applications on [0,one million], then f is a non-end function on [0,one million] be conscious that f(0) = g(0) - h(0) > 0 and f(l) = g(l) - h(l) < 0. this means that 0 is a extensive style between f(0) and f(l). by skill of the Intermediate cost Theorem, there exists a extensive style x* such that f(x*) = 0. f(x*) = 0 -> g(x*) - h(x*)= 0 -> g(x*) = h(x*) for some x* in [0,one million]

Answer 3

- It is a continuous line (no holes, no separate segments)
- There is a symmetrical function (the inverted) with respect to the y=x axis.

Answer 4

It is strictly monotone (it may be either increasing or decreasing, but if it is invertible and continuous is is impossible that it increase over one interval and decrease over a second, or vice versa).

Answer 5

Symmetry

f( f'(x)) = x and f' (f(x)) = x
Note f'(x) -in not a first derivative of f(x) it represts an inverse of f(x).