Is 3 + root 2 a fraction

Is 3 + root 2 a fraction

No, a number is rational if it can be expressed as a fraction
If a number is rational, it must be expressed in fractional form
For example, 0.1 cycle, = 1 / 9
Because radical 2 is irrational (provable), so 3 + radical 2 is irrational, so it cannot be expressed as a fraction
Discuss the continuity of function: F (x, y) = sin (XY) / Y (y is not equal to zero) 0 (y is equal to zero)
Where y = 0 (i.e. the point on the x-axis), if the origin (0,0), from | sin (XY) / y|
If the function y = f (x) has an inverse function, then the following statement about the root of the equation f (x) = a (a is a constant) is correct ()
A. There is only one real root B. there is at least one real root C. There is at most one real root d. There is no real root
I chose a, but the answer is C. can you give me a counterexample,
f(x)=x.x,x>0 a
Y = x power of E, a = 0
Given the function f (x) = X3 ax + 3x + B, if the tangent of the function image at x = 1 is parallel to the X axis, for X at - 1
When f '(x) = 3 (x2) + 3-A ∵ the tangent at x = 1 is parallel to X axis ∵ x = 1, f' (x) = 0, i.e. a = 6
∴f'(X）=3(X2)-3; f(x)=x3-3x+b
When f '(x) > 0, the range of F' (x) is (- ∞, - 1) ∪ (1, + ∞); f '(x) f' (1), f (4) > F '(4) b > 2, f (0) = b ∪ f (0) > 2
The tangent at x = 1 is parallel to the X axis, which means that the initial derivative is 0 at this point, that is, 3-2a + 3 = 0, so a = 3.
Y = f (x) - f '(x) = x ^ 3 + 9x + B-3 > = 0, the derivative of y = 3x ^ 2 + 9 (constant greater than 0), so y is monotonically increasing in [1,4], and has the minimum value B + 7 > = 0 at x = 1, so b > = - 7
So, f (0) = b > = - 7
If the function y = f (x) (x ∈ D, y ∈ a) has an inverse function y = f ^ - 1 (x) (x ∈ a), then does the equation f (x) = f ^ - 1 (x) have roots? What is the law of roots
If a function has an inverse function, then the original function must be symmetric with its inverse function with respect to y = X,
So if the equation f (x) = f ^ - 1 (x) has roots, it must be on the line y = X,
So whether the equation has roots is equivalent to whether y = f (x) and y = x have intersections, that is, whether x = f (x) has roots,
If x = f (x) has roots, then f (x) = f ^ - 1 (x) has roots
On the contrary, there is not
The combination of number and shape
If y = f (x) is a decreasing function and f (A-3) + F (9-a2) < 0, then the value range of a is ()
A. (22，3)B. (3，10)C. (22，4)D. （-2，3）
∵ function is an odd function with the domain of definition (- 1,1) ∵ - f (x) = f (- x) and ∵ y = f (x) is a decreasing function, ∵ inequality f (A-3) + F (9-a2) < 0 can be reduced to: F (A-3) < f (9-a2), that is, f (A-3) < f (a2-9), that is, − 1 < a − 3 < 1 − 1 < A2 − 9 < 1a − 3 > A2 − 9, and the solution is a ∈ (22,3), so choose: a
What is the inverse function of y = 2x
The properties of y = x / 2 inverse functions are as follows: (1) the images of two functions which are inverse functions are symmetric with respect to the straight line y = x; (2) the necessary conditions for the existence of inverse functions are that the domain of definition and the range of value of functions are one-to-one mapping; (3) the monotonicity of a function and its inverse functions is consistent in the corresponding interval; (4) most even functions
The function y = f (x) is a decreasing function on (- 1,1) and an odd function satisfying f (a2-a-1) + F (A-2) > 0. Try to find the range of A
From the topic meaning, f (a2-a-1) + F (A-2) > 0, that is, f (a2-a-1) > F (A-2), and the function y = f (x) is odd, so f (a2-a-1) > F (2-A), and the function y = f (x) is a decreasing function on (- 1, 1), so there is − 1 < A2 − a − 1 < 1 − 1 < a − 2 < 1A2 − a − 1 < 2 − a, {− 1 < a < 0 or 1 < a < 21 < a < 3 − 3 < a < 3} 1 < a < 3, so the value range of a is {1 < a < 3 Yes (1, 3)
Are y = 2x and y = 1 / 2x reciprocal functions? I think they are right, but the answer is wrong. Why?
The answer is wrong, you are right
The inverse function of y = 2x is x = 2Y
In general, we set X as an unknown quantity and y as a function. According to the custom, the inverse function should be y = x / 2
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From y = 2x, we can know that x = Y / 2, so the inverse function of y = 2x is y = x / 2.
The function y = f (x) is a decreasing function on (- 1,1) and an odd function satisfying f (a2-a-1) + F (A-2) > 0. Try to find the range of A
From the topic meaning, f (a2-a-1) + F (A-2) > 0, that is, f (a2-a-1) > F (A-2), and the function y = f (x) is odd, so f (a2-a-1) > F (2-A), and the function y = f (x) is a decreasing function on (- 1, 1), so there is − 1 < A2 − a − 1 < 1 − 1 < a − 2 < 1A2 − a − 1 < 2 − a, {− 1 < a < 0 or 1 < a < 21 < a < 3 − 3 < a < 3} 1 < a < 3, so the value range of a is {1 < a < 3 Yes (1, 3)