What is the inverse function of F (x) = (x + 1) inx-x + 1?

Let any point (x, y) on the original function f (x), the symmetric point on the image of the inverse function is (x ', y')
For y = x symmetry, then x '= y y' = x and y = (x + 1) lnx-x + 1, so x '= (y' + 1) LNY '- y' + 1
The inverse function x = (y + 1) lny-y + 1 is obtained by changing X 'and y' into x and y

1. Inverse function of F (x) = in (x2-1), (x > 1) 2. Y = inverse function of INX + 1 (x > 0)

F (x) = in (x2-1), (x > 1) y = √ (e ^ x + 1) (x belongs to R)
Y = INX + 1 (x > 0) y = e ^ (x-1) (x belongs to R)

A necessary and sufficient condition for the existence of inverse function on interval [1.2] for function f (x) = x ^ 2-2ax-3

If there is an inverse function, then f (x) is monotone
So the axis of symmetry is not in the interval (1,2)
Axis of symmetry x = a
So a = 2

The necessary and sufficient condition for the existence of inverse function on interval [1,2] of function f (x) = x2-2ax-3 is () A. a∈（-∞，1] B. a∈[2，+∞） C. α∈[1，2] D. a∈（-∞，1]∪[2，+∞）

Analysis: the symmetry axis of ∵ f (x) = x2-2ax-3 is x = a,
⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆⊆ [a, + ∞) if and only if y = f (x) has an inverse function on [1,2],
That is, a ≥ 2 or a ≤ 1
Answer: D

Original function derived from continuous inverse function? Is the inverse function of the inverse function equal to the original function? Is there a rule? Can people solve the problem of knowing by the way~

Example: find the inverse function of y = 3x-2, the definition domain of y = 3x-2 is r, and the range of value is R. from y = 3x-2, x = (y + 2) / 3. If x and y are exchanged, then the inverse function of y = 3x-2 is y = (x + 2) / 3 (x belongs to R). Just like the example, the inverse function of a function, generally speaking, is to exchange the positions of X and y to get this function

Is the inverse function the same as the original function

The parity of functions with inverse functions is invariant
Monotonicity is also unchanged
In fact, only odd functions have inverse functions, even functions have no inverse functions
Similarly, functions that are not monotonic have no inverse functions

Must the parity of a function and its corresponding inverse function be the same?

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The properties of inverse function: (1) the images of two functions which are reciprocal functions are symmetric with respect to the straight line y = x; (2) if and only if a function has an inverse function, if and only if the function is monotone in its domain of definition; (3) a function and its inverse function have the same monotonicity in the corresponding interval; (4) even function must not exist

How to judge the parity of original function and inverse function? As the title

The inverse function of odd function is odd function, and non single valued even function has no inverse function

The parity of inverse functions,

If the original function is odd, then the inverse function is still odd
Even functions have no inverse functions
The original function and the inverse function have the same monotonicity

What is the inverse function of F (x) = (x + 1) inx-x + 1?