A line passing through the origin O and the image of the function y = log (8) x It is proved that the point P, Q and origin o are on the same line

A line passing through the origin O and the image of the function y = log (8) x It is proved that the point P, Q and origin o are on the same line

Let y = log (8) x = 1 / 3 * log (2) x let the equation of straight line be y = KX, and the intersection point (x1, kx1), (X2, kx2) kx1 = log (8) x1, kx2 = log (8) x2 respectively cross m, n as the parallel line of Y axis and intersect with the image of function y = log (2) x, then the abscissa of P and Q is x1, and the ordinate is log (2) X1 = 3log (8) X1 = 3kx1

Given that G (x) = (a + 1) ^ (X-2) + 1, (a is greater than 0), the image crosses point a, and point a is on the image of function f (x) = log root 3 (x + a) F (x) = log root 3 (x + a) = log (x + a) / log root 3

A number that is not equal to 0 is equal to 1 to the power of 0
A is greater than 0, so a + 1 is not equal to 0
So (a + 1) ^ 0 = 1
So when X-2 = 0, y = 1 + 1
So a (2,2)
Substituting f (x)
2=log√3(2+a)
So (√ 3) ^ 2 = 3 = a + 2
A=1
So g (x) = 2 ^ (X-2) + 1

Given the function f (x) = log (x + radical 1 + x ^ 2), judge the parity of F (x) As the title We must first prove the symmetry of the domain

Odd function
prove:
F (- x) = log ((radical 1 + x ^ 2) - x)
=Log (1 / x + radical 1 + x ^ 2) (molecular rationalization)
=-Log (x + radical 1 + x ^ 2)
=-f(x)
Get the certificate

The graph of the function g (x) = (a + 1) ^ (X-2) + 1 (a > 0) is constant over the fixed point a, and the point a is in the graph of the function f (x) = log root 3 (x + a) (1) Find the real value range of (2) (2) of (2) | (3) When | g (x + 2) - 2 | 2B has two unequal real roots, find the value range of B Wrong number. Sorry

(1) It is easy to know that G (x) passes through the fixed point (2,2), and substituting f (x) leads to a = 1
(2) Because the root three is greater than one, f (x) x + a > 0, x > - 1
So - 1 (3) a = 1 can be substituted into the equation, (what is b)

If the inverse scale function y = 6 / x, the distance between a point P and the origin is root 13, and the coordinates of point P are obtained

P(x,y)
The distance from the origin is ^ 2 = 2;
Namely
x^2+（6/x）^2=13；
x^4+36=13x^2;
x^4-13x^2+36=0;
(x^2-4)*(x^2-9)=0;
X ^ 2 = 4; or x ^ 2 = 9;
X = + - 2; or x = + - 3;
p(2,3)(-2,-3);(-3,-2);(3,2)

On the image of inverse scale function y = 6 / x, how many points are there whose distance to the coordinate origin o is equal to the root sign 11? What are their respective? Please give examples and language to explain in detail

If the point is (x, y), then when x = y, the point is closest to the origin; if xy = x? = 6, then x? + y? = 12 ﹥ 11, it does not exist

The inverse proportional function y = k is known A point P on the image of X (k > 0) has a distance OP = 2 from the origin o If the area of △ OPQ is 4 square units, we can find: (1) the coordinates of point p; (2) the analytic formula of the inverse scale function

Let P coordinate be (a, KA). Then OQ = | a | a |, PQ = 124\\\\\124\\\124\\\124\124\124124124124124124124124124124124124124124124124\a2 + (8a) 2 = 25

If there is a point P (m, n) and M + n = 3 on the image of the inverse scale function y = K / x, and the distance from the point P to the origin is root 13, then the analytic formula of the inverse scale function is

m+n=3
m^2+n^2=13
simultaneous equation
(m+n)^2=9
2mn=-4
mn=-2
k=xy
So k = Mn = - 2
y=-2/x
You see

What is the value range of the independent variable in the function y = root X-1 To explain

1 / (x-1) greater than or equal to 0
And X-1 is the denominator, so it can't be equal to 0
So X-1 is greater than 0
X is greater than 1

The value range of the independent variable X of X + 1 under the root of function y = X-1 is____ ?

y=√(x+1)/(x-1)
Denominator is not 0: X-1 ≠ 0 x ≠ 1
Molecule: x + 1 ≥ 0 x ≥ - 1
Value range: X ≥ - 1 and X ≠ 1