The problem of function image, the problem of function image symmetry, please write the proof in detail, 1. What is the symmetry between the image of function y = f (x-1) and the image of function y = f (1-x) 2. What is the symmetry between the image of function y = - f (x-1) and the image of function y = f (1-x) The first one I think is about x = 1 symmetry. I got it by enumerating. I made f (x) = x, X & # 178;, 1 / X try to get it. I know how to prove it first Second, I gave some examples, but I didn't get them. I also want to prove them

The problem of function image, the problem of function image symmetry, please write the proof in detail, 1. What is the symmetry between the image of function y = f (x-1) and the image of function y = f (1-x) 2. What is the symmetry between the image of function y = - f (x-1) and the image of function y = f (1-x) The first one I think is about x = 1 symmetry. I got it by enumerating. I made f (x) = x, X & # 178;, 1 / X try to get it. I know how to prove it first Second, I gave some examples, but I didn't get them. I also want to prove them

1、
Let t = X-1,
Then 1-x = - T
Because the image of y = f (T) and the image of y = f (- t) are symmetric with respect to t = 0
So the image of the function y = f (x-1) and the image of the function y = f (1-x) are symmetric with respect to 1-x = 0, that is, x = 1
2、
As above, let t = X-1
Because the image of y = f (T) and the image of y = - f (- t) are symmetrical about the origin (t = 0, y = 0)
So the image of the function y = - f (x-1) and the image of the function y = f (1-x) are symmetric with respect to point (1,0)

What is the symmetry of the image of the function y = sin (x + 3 Π / 2)?

y=sin(x+3π/2)=-cosx
[odd variable, even constant, sign in quadrant]
So the axis of symmetry is x = k π [the point where y = + - 1]

Given the function f (x) = the x power of a plus (x + 1) parts (X-2) (a > 1), we prove that f (x) is a function on (- 1, positive infinity)

f(x)=a^x+(x-2)/(x+1)
f'(x)=a^x(lna)+3/(x+1)^2
When x > - 1, f '(x) > 0, so it is (- 1, positive infinity) monotone increasing