If the power function y = f (x) is known, then f (9)=

If the power function y = f (x) is known, then f (9)=

Let y = f (x) = x ^ n
∵ the image of function y = f (x) passes through the point (2, √ 2),
∴y=f(2)=2^n
That is, 2 ^ n = √ 2
2^n=2^(1/2)
∴n=1/2
Then y = f (x) = x ^ (1 / 2)
Then f (9) = 9 ^ (1 / 2) = 3
Given that the image of power function y = f (x) passes through (2, root 2), the analytic expression of power function is
Let: the power function y = f (x) = x ^ A, the image passes through (2, root 2), then there is 2 ^ a = root 2 = 2 ＾ (1 / 2), and a = 1 / 2 is obtained
Then the analytic expression of power function is f (x) = x ^ (1 / 2)
After (2, √ 2), it shows that when x = 2, y = √ 2, that is, y = x ^ 1 / 2, which is the analytical formula
Because the function is a power function, let its analytic formula be y = x ^ A, and it should be the image passing point (2, root 2) of the function
Root 2 = 2 ^ A, solution: a = 1 / 2
Therefore, the analytic formula of the function is: y = x ^ (1 / 2) (y = x to the power of two parts)
Three rational numbers a, B, C and abc0 are known. When x = "a" / A + "B" / B + "C" / C, find the value of the 19 cube minus 92x plus 2 of the algebraic formula X
abc0
So there are two positives and one negation in ABC
x=|a|/a+|b|/b+|c|/c
=1+1-1
=1
x^19-92x+2
=1-92+2
=-89
Because the product of ABC is negative, there must be odd negative numbers, that is, there are two cases
1.3 numbers are all negative
2.2 positive numbers and 1 negative number
And the sum of ABC is a positive number, so the first case can't be two positive numbers and one negative number
So x = 1 + 1-1 = 1
So the 19th power of X - 92x + 2 = - 89
abc0
So there are two positives and one negation in ABC
x=|a|/a+|b|/b+|c|/c
=1+1-1
=1
x^19-92x+2
=1-92+2
=-89
When m is a value, the function y = (M & # 178; - m-2) x ^ m & # 178; - 5m + 4 + (m-1) x + M?
2. If the function y = (A-1) x ^ B + 1 + X & # 178; + 1 is a quadratic function, find the value range of a and B. my mother will turn off the computer soon! Baby! For my life! Help me
1. If this function is a linear function, find the value of M
M ^ 2-m-2 = 0, M-1 is not equal to 0
Then: M = 2
2. If this function is a quadratic function, how to find m
M ^ 2-m-2 is not equal to 0
Then: m is not equal to 2, M is not equal to 1
To put the upper end of the 5-meter-long ladder on the edge of the balcony 3 meters above the ground, guess the minimum gradient of the ladder______ .
It is known that the horizontal distance between the ladder and the balcony is 4m, then the gradient is vertical height: horizontal length = 3:4. The minimum gradient of the ladder is 34
Let f (x) = (x-2011) (x-2012) + 1 / 2013, then f (x) = 0, why are the two solutions in (20112012)
G (x) = (x-2011) (x-2012) = 0 is 20112012f (x) = (x-2011) (x-2012) + 1 / 2013, which means g (x) moves upward by 1 / 2013 units. G (x) is a quadratic function graph with an opening upward, intersecting the X axis at two points in 20112012, and then moving upward. When you make the image, you will find that the intersection point with the X axis will be closer to the middle
f(x)=(x-2011)(x-2012)+1/2013=0
Then (x-2011) (x-2012) = - 1 / 2013
To make the product of two factors negative, one factor is positive and the other is negative
If it is greater than 2012, both factors are positive
If it is less than 2011, both factors are negative
So the solution is somewhere in between
If the power function f (x) = (M & # 178; - m-1) x Λ (M & # 178; + M-3) is an increasing function at (0, + ∞), then f (- 1 / 2)=
The coefficient must be 1, m ^ 2-m-1 = 1, m-2 (M + 1) = 0, M = 2, - 1
When m = 2, f (x) = x ^ 3, where x > 0 is an increasing function, f (- 1 / 2) = - 1 / 8
When m = - 1, f (x) = x ^ (- 3), where x > 0, it is a decreasing function
So f (- 1 / 2) = - 1 / 8
An acute angle trigonometric function problem in the third year of junior high school,
If α is an acute angle and satisfies Tan & sup2; α - (1 + √ 3) Tan α + √ = 0, find the degree of ∠α
The "√" in the back should be √ 3, right?
Because Tan & sup2; α - (1 + √ 3) Tan α + √ 3 = 0
Decomposition of factor
(tanα－1)(tanα－√3)＝0
therefore
(Tan α - 1) = 0, or
(tanα－√3)＝0
therefore
Tan α = 1, or tan α = 3
Because α is an acute angle
So α = 45 degrees
Or α = 60 degrees
There seems to be a formula. You go to the book
Let f (x) be a function defined on R, f (x) = [1 + F (X-2)] / [1-f (X-2)], and f (3) = 2 + √ 3, then f (2011) =?
First, find the rule f (3) = 2 + √ 3f (5) = [1 + F (3)] / [1-f (3)] = - √ 3f (7) = [1 + F (5)] / [1-f (5)] = - 2 + √ 3f (9) = [1 + F (7)] / [1-f (7)] = √ 3 / 3f (11) = [1 + F (9)] / [1-f (9)] = 2 + √ 32
How does the root sign (the 2nd power of a - (the 2nd power of a / 2)) become (the root sign (3) / 2) multiplied by a
Root sign (2nd power of a - (2nd power of a / 2))
The first step is radical, = a - (A / 2)
so what?
How does a - (A / 2) become (radical (3) / 2) * a
Friends, a ^ 2 = (4 * a ^ 2) / 4
(a/2)^2=(1*a^2)/4
Subtracting them is equal to (3 * a ^ 2) / 4
If a > 0, then the result is equal to: root 3 * A / 2 if a > 0
First silence, then silence.
Root sign (2nd power of a - (2nd power of a / 2)) = root sign (2nd power of A-A2 / 4)
=Root sign [3 (2nd power of a) / 4]
=(root (3) / 2) multiplied by a
This is just a simple conversion. It seems that you need to do more calculation
The root of the second power of a - (A / 2) becomes the root (3) / 2) multiplied by A