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It is known that the image of the quadratic function y = (m-1) x2 + M2-1 with respect to x passes through (0,3) and the parabolic opening is downward (1) Find the value of M; (2) Find the distance between the two intersections of this parabola and the X axis Now,
The image of y = (m-1) x ^ 2 + m ^ 2-1 passes through (0,3):
3=0+m^2-1
Parabolic opening downward:
m-1＜0
M ^ 2 = 4 and m < 1
m=-2
y=（-2-1）x^2+(-2)^2-1 = -3x^2+3=-3(x+1)(x-1)
x1=-1,x2=1
x2-x1=1-(-1)=2
Distance between two intersections of parabola and X axis 2
The function f (x) = |lgx, (010) is known. If a, B and C are not equal to each other, and f (a) = f (b) = f (c) Known function f (x) = |lgx| (0 < x ≤ 10)- 1 / 2x + 6, (x > 10). If a, B and C are not equal to each other and f (a) = f (b) = f (c), the value range of ABC is A （1,10） B （5,6） C （10,12） D （20,24）
|lga|=lg|b|=-1/2c+6 00 -1/2x+6>0 x
Given that f (x) = √ 9-x ^ 2 (x > = 0) and the and function f (x) = lgx g (x) = 10 ^ x, the focus is p (x1, Y1) Q (X2, Y2), then X1 ^ 2 + y ^ 2 =? x1^2+x2^2=？
F (x) = root sign (9-x ^ 2) (x > = 0), FX ^ 2 = 9-x ^ 2, FX ^ 2 + x ^ 2 = 9, that is, it is a circle with the origin as the center and radius of 3, and its range is in the first quadrant. F (x) and G (x) are inverse functions of each other, that is, their curves are symmetrical about y = x and FX is symmetrical about y = x, so their intersection points are symmetrical about y = x
Known function f (x ^ 2-3) = lgx ^ 2 / x ^ 2-6 (1) Expression and definition field of y = f (x) (2) Judge the parity of function y = f (x) and prove it
（1）∵f（x ²- 3）=lgx ²/ （x ²- 6）∴x ²/ （x ²- 6) ＞ 0, i.e. x ²＞ 6, make x ²- 3 = t (T > 3), then x ²= The expression and definition field of T + 3 ‡ f (T) = LG (T + 3) / (T-3) ‡ y = f (x) = LG (x + 3) / (x-3) ‡ y = f (x) are:
Known function f (x) = 10 ^ x, (x ≤ 0); Lgx, (x > 0), then f [f (1 / 2)]=
f(x)=10^x,(x≤0); lgx,(x>0),
If f (1 / 2) = LG (1 / 2) = - LG20 and a ≠ 1, n > 0, then a ^ (Logan) = n
Let f (x) = |lgx|, a and B be real numbers satisfying f (a) = f (b) = 2F ((a + b) / 2), where 0
(1) : because a is not equal to B, LGA is not equal to LGB, and | LGA | = | LGB |, it must be LGA = - LGB = LG (1 / b), so a = 1 / B, because 0
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