What is the range of the function y = 2 radical x + 1 / 2 radical x

What is the range of the function y = 2 radical x + 1 / 2 radical x

y=√x/(2√x+1)
Let t = √ x > = 0
y=t/(2t+1)=0.5-0.5/(2t+1)
t>=0, 0

How to calculate the coefficient of logarithm of product quotient power? For example, logarithm of 2 of 3log7 - logarithm of 9 of log7

3log(7)2-log(7)9=log(7)8-log(7)9
=log(7)(8/9)

If we know that the image of the function y = ax + 4 and y = bx-2 intersects at a point on the x-axis, then a △ B is equal to?

First of all, if two functions intersect on the X axis, then y value is 0, 0 = ax + 4, the solution is x = - 4 / A, 0 = bx-2. The solution is x = 2 / b. since the two X values intersect at a point, they should be equal, so - 4 / a = 2 / B, the solution is a = - 2b, then a △ B is equal to - 2b △ B = - 2. I hope you understand

Given that a (- 2,7), B (1,1), the vertex of the parabola is on the y-axis, find the function expression

The solution is as follows
The vertex of the parabola is on the y-axis, which means that the symmetry axis is y-axis, that is: - B / 2A = 0, B = 0
Let the parabola function be y = ax ^ 2 + C
Substituting a and B coordinates:
7=4a+c
1=a+c
A = 2, C = - 1
So the parabola function relation is y = 2x ^ 2 - 1

Given x = (4-root 7) / 3, then find the value of (x ^ 4 + x ^ 2 + 1) / x ^ 2

Given x = (4-root 7) / 3, then find the value of (x ^ 4 + x ^ 2 + 1) / x ^ 2
X = (4-radical 7) / 3 so
X & # 178; = (16 + 7 - 8 pieces 7) / 9
=(23 - 8 pieces, 7) / 9
1 / X & # 178; = = 9 / (23 - 8 pieces, 7)
=9 (23 + 8, 7) / 81
=(23 + 8 pieces, 7) / 9
So (x ^ 4 + x ^ 2 + 1) / x ^ 2
= x² +1 + 1/x²
== (23 - 8 7) / 9 + 1 + (23 + 8 7) / 9
= ( 23+23 ) / 9 +1
= 46/ 9 + 1
=55 out of 9
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I have a little test, please click next to the answer
"Choose as satisfactory answer"

1. Without changing the value of the fraction, the coefficients of the numerator and denominator of the fraction 0.1 x + 0.2 Y / 0.3 x + y are changed into integers_____ .
2. When_____ The simplest common denominator of fractions x + 1 / (X-2) (x-1) and x-3 / (x + 6) (x-1) is______ 4. If x

1. Without changing the value of the fraction, the coefficients of the numerator and denominator of the fraction 0.1 x + 0.2 Y / 0.3 x + y are changed into integers to get (x + 2 y) / (3 x + 10 y)_____ .
2. When___ X is not equal to 2 / 3__ The fraction X-1 / 2-3x is significant
3. The simplest common denominator of fractions x + 1 / (X-2) (x-1) and x-3 / (x + 6) (x-1) is_ (x-2)(x-1)(x+6)_____ .
4. If x

Help me solve the quadratic equation of one variable - 1 / 2x ^ 2 + √ 2 / 2x + 2 = 0, thank you
thankyou!

Double by (- 2)
x²-√2x-4=0
(x-2√2)(x+√2)=0
x=2√2,x=-√2

3a of 4B times 2b of 9A + 2x of X + 2x of X divided by the square of X - the square of X + 2x of X
Find out the simplest common denominator A-B / A, the square of a-Ab / b
X squared + 2x + 1 / x, X squared - 1 / x + 2

3a of 4B times 2b of 9A = 3A / (4b) × 2B / (3a) &# 178; = 1 / (6a) x's square + 2x + 1 / X divided by X's Square - 1 / X's square + 2x = x / (x + 1) &# 178; △ x (x + 2) / (x + 1) (x-1)] = [x (x + 1) (x-1)] / [x (x + 1) &# 178; (x + 2)] = (x-1) / (X & # 178; + 3x + 2) = (x-1) / (X & # 178; + 3x + 2)

Xiaofang saw such a problem in Xiaoli's typical exercise excerpt: when x = - 1 / 4, y = 0.78, find the value of polynomial 6x ^ 3-5X ^ 3Y + 2x ^ 2Y + 2x ^ 3 + 5x ^ 3y-8x ^ 3 + 7. Xiaofang said to Xiaoli: "the condition given in the Title X = - 1 / 4, y = 0.78 is redundant." is Xiaofang reasonable? Why?

That's right. When the polynomials are combined, you will find that except for 7, the other values are 0. When 0 + 7 is used, the answer given in the question is unnecessary

How to prove that the determinant of matrix A is 0

To the contrary
Suppose | a * | is not equal to 0, then a * is reversible
From AA * = |a|e = 0
The inverse matrix of right multiplication a * on both sides of an equation
A = 0
So a * = 0
So | a * | = 0
So when | a | = 0, | a * | = 0