Function f (x) = LG1 − x The parity of 1 + X is __

By 1 − x
1 + X ＞ 0, the solution is: - 1 ＜ x ＜ 1,
The definition domain of function f (x) is (- 1, 1), which is symmetrical about the origin,
∵ f (x) = ln1 + X
1−x=-ln1−x
1+x=-f（x），
The function f (x) is an odd function,
So the answer is: odd function

Judging function parity by definition 1) Y = g (x) has g (a + b) = g (a) + G (b) for all real numbers a and B 2) The function H (x) satisfies that h (x + y) + H (X-Y) = 2H (x) * H (y). (x belongs to R, y belongs to R) and H (0) is not equal to 0

1. Since a and B are true for all real numbers, let a = 0 and B = 0
g(0+0)=g(0)+g(0)
g(0)=2g(0)
g(0)=0
Let a = - B G (- B + b) = g (- b) + G (b)
g(0)=g(-b)+g(b)
Because g (0) = 0 (certified), 0 = g (- b) + G (b)
g(-b)=-g(b)
So it's an odd function
2. Since x belongs to R and Y belongs to R, let x = 0 and y = 0
h(0+0)+h(0-0)=2h(0)*h(0)
h(0)=1
Let x = 0 h (0 + y) + H (0-y) = 2H (0) * H (y)
Because H (0) = 1 (certified), H (y) + H (- y) = 2H (y)
h(-y)=h(y)
So it's an even function

What does function parity mean? How to understand?

The image of odd function is symmetrical about the origin;
The image of the even function is symmetric about the y-axis;
When some laws have parity, it means that we only need to understand half of the law to master all the laws

Judgment function f (x) = LG（ Parity and monotonicity of x2 + 1-x)

because
X2 + 1 > x, so the definition field of F (x) is r,
Because f (- x) + F (x) = LG（
x2+1+x)+lg(
x2+1-x)=lg(
x2+1+x) (
x2+1-x)=0
So f (- x) = - f (x), so f (x) is an odd function
Ling y=
X2 + 1-x, then y '= 2x
two
X2 + 1-1 < 0, so y=
X2 + 1-x is a subtractive function,
F (x) is known as a subtractive function from the monotonicity of the composite function

Known function f (x) = lg|x| (1) Judge the parity of F (x); (2) Draw a sketch of function f (x) and point out the monotonic interval of function f (x)

(1) From the solution of | x | > 0, X ≠ 0 is obtained,
The definition domain of the function is (- ∞, 0) ∪ (0, + ∞)
∵f（-x）=lg|-x|=lg|x|=f（x），
‡ f (x) is an even function
(2) Since f (x) is an even function, its image is symmetric about the Y axis
The monotone decreasing interval of F (x) is (- ∞, 0) and the monotone increasing interval is (0, + ∞)

Function f (x) = LG1 − x The parity of 1 + X is __