For any real number k, the image of the function y = K (x2-1) + x-a has a common point with the x-axis

For any real number k, the image of the function y = K (x2-1) + x-a has a common point with the x-axis

The function image and X-axis have a common point, that is to say, the equation y = 0 has a real solution
The deformation of the function is y = K (x ^ 2) - X - (a + k)
Let y = 0,
① If k = 0, then the equation becomes - x-a = 0,
The solution is x = - A, and the range of a is r;
② If K ≠ 0, then y = 0 is a quadratic equation with one variable, and its discriminant should be △ 0 or more,
That is △ = 1 + 4K (a + k) = 4K ^ 2 + 4ak + 1 = (2k + a) ^ 2 + 1-A ^ 2 ≥ 0,
If △≥ 0 is constant, then 1-A ^ 2 ≥ 0,
The solution is - 1 ≤ a ≤ 1
In conclusion, a should satisfy a ∈ [- 1,1]

If any x belongs to the real function f (x) = x ^ 2 + x-a + 1, the image and X axis always have a common point, the value range of real number a can be obtained

The domain of F (x) is r,
The image is a parabola with the opening upward,
Its minimum value is f (- 1 / 2) at the vertex of parabola
When the meaning of the question is satisfied,
f(-1/2)≤0
That is 1 / 4-1 / 2-A + 1 ≤ 0
Solution
a≥3/4.
Of course, it can also be solved by discriminant
F (x) and X-axis always have a common point,
Then f (x) = 0 has a real root,
therefore
△=1+4(a-1)≥0
The solution is a ≥ 3 / 4
Big brother, that x is an arbitrary value,
How much x equals does not affect the intersection of F (x) and X axis,
What is the value of X? What is the value of the function,
When x = 0, f (0) = - A + 1

It is known that a nonzero function f (x) has f (a + b) = f (a) f (b) for any real number ab
When f (1) = 1 / 16, the inequality f (x-3) * f (5) ≤ 1 / 4 is solved

If x 1. If f (4) = 1 / 16, solve the inequality f (x-3) * f (5) f (x) = f (x / 2) ^ 2 > 0 (because the function is non-zero, f (x / 2) ≠ 0) 2. Let a = 0, B = 0f (0) = f (0) ^ 2, f (0) = 1, let a = x, B = - x, f (0) = f (x) f (- x)

If the odd function f (x) is a decreasing function in the interval [- 3, - 2] and the maximum value is 6, then f (x) is a decreasing function in the interval [2,3]____ What is the minimum value of the function

Is a decreasing function with a minimum of 6