The negation of the proposition "the image of the original function and the inverse function is symmetric with respect to y = x" is______ ．

The negation of the proposition "the image of the original function and the inverse function is symmetric with respect to y = x" is______ ．

Suppose that the full Quantifier "all" is implied in the question. Therefore, the negation of the question is that there exists an original function, and the conclusion is that the image of the original function and the inverse function is not symmetrical about y = X. the negation of the original proposition is that there exists an original function and the image of the inverse function is not symmetrical about y = X

If the image of inverse function F-1 (x) of F (x) = (A-X) / (x-a-1) is centrosymmetric with respect to the point (- 1,1 / 2), then the value of real number a is equal to ()

F (x) = (A-X) / (x-a-1) = - 1 + (- 1) / (x-a-1). According to the definition of inverse function, if you use y to express x, you can get x = (- 1) / y + 1 + A + 1. I don't need to play the rest

If the image of inverse function F-1 (x) of F (x) = (A-X) / (x-a-1) is centrosymmetric with respect to the point (- 1,1 / 2), then the value of real number a is equal to ()

This problem only needs to solve the value of a, you can try it directly
For example, if x = a, then point (a, 0) is on f (x)
So (0, a) is on F-1 (x), so the centrosymmetric point (- 2,1-a) is also on F-1 (x), that is to say, (1-A, - 2) satisfies f (x)
If we take in the equation, we can solve a = - 1 / 2

Know the vertex coordinates and the solution of a root how to find quadratic function analytic expression

Let y = a (x + 2) ^ 2 + 0;
Then (1, - 2) is taken into the quadratic function above
So, the quadratic function is y = - 2 / 9x ^ 2-8 / 9x-8 / 9
This method seems simpler

The vertex coordinates of a quadratic function are (2,3) and pass through the point (3,1). Find the analytic expression of the quadratic function

According to the sentence of vertex coordinates of quadratic function, the function can be set as y = a (X-2) ^ 2 + 3, and then (3,1) is brought in. It is found that a = - 2, then the function is y = - 2 (X-2) ^ 2 + 3, expanded into y = - 2x ^ 2 + 8x-5