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If the maximum value of function y = a ^ (2x) + 2A ^ X-1 (a > 0, a ≠ 1) on interval [- 2,2] is 14, then the value of real number a is 14 Root 3, 3 / 3 root 3
Let a ^ x = t, if a > 1, y = f (T) = T ^ 2 + 2t-1, the maximum value of [1 / A ^ 2, a ^ 2] is 14
If 0
If the function f (x) = x ^ 2 + BX + C has f (1 + x) = f (1-x) for any real number, what is the size relationship between (0). F (1). F (4)?
Thinking of solving problems
f(1+x)=f(1-x)
So f (x) is symmetric with respect to x = 1
F (x) is a quadratic function with an opening upward
X = 1 is the axis of symmetry, so f (1) is the minimum
x> When f = 1, f (x) is an increasing function
f(0)=f(1-1)=f(1+1)=f(2)
Because 4 > 2 > 1
So f (4) > F (2) > F (1)
So f (4) > F (0) > F (1)
If the function f (x) = x * x + BX + C has f (2 + x) = (2-x) for any real number, then f (1), f (2), f (4) have the same size
F (2 + x) = f (2-x) shows that f (x) is symmetric about the straight line x = 2, that is, the axis of symmetry of the parabola is the straight line x = 2, because the opening is upward, so the closer the independent variable is to the straight line x = 2, the smaller the function value is, so f (2)
If the function f (x) = x ^ 2 + BX + C has f (2 + x) = f (2-x) for any real number x, then the size relations of F (2), f (1) and f (4) are__
What I want to ask is why his axis of symmetry x = 2. I just need to ask about the axis of symmetry. I need to be super clear about the rest, not to mention the axis of symmetry
What is an axis of symmetry? In a simple and popular way, it is the point on both sides of the axis where the distance from the axis is equal, and the value of the function at those two points is equal. Take an example: x = 2 is the axis of symmetry, and the distance a between the left and right sides of x = 2 is equal, that is, f (2-A) = f (2 + a). This is why when you see f (2 + x) = f (2-x), you can know why x = 2 is the axis of symmetry
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