Given the function y = f (2x-1), ask whether the independent variable is x or 2x-1? Given the domain of y = f (2x-1), how to find the domain of F (x)? Given the domain of y = f (x), how to find the domain of F (2x-1)?

Given the function y = f (2x-1), ask whether the independent variable is x or 2x-1? Given the domain of y = f (2x-1), how to find the domain of F (x)? Given the domain of y = f (x), how to find the domain of F (2x-1)?

The independent variable is 2x-1
The domain of X can be obtained by directly putting 2x-1 into the known domain and solving the inequality
Similarly, when x is put into a known domain and transformed to 2x-1 by multiplying 2 and subtracting 1 on both sides, the domain on both sides of the unequal sign is 2x-1

Y = x & sup2; - 2x-3 = 0, when x takes what value, the function value is greater than 0, when x takes what value, the function value is less than 0

When x is greater than 3 or X is less than - 1, the function value is greater than 0; when x is greater than - 1 and less than 3, the function value is less than 0

It is known that when the value of quadratic function y = x2-2x-3 is 0, the value of independent variable x is obtained
(2) When the function value is equal to 4, find the value of the independent variable x. (3) can the function value be equal to - 5? Why

① ∵ y = x & sup2; - 2x-3 ∵ when y = 0, X & sup2; - 2x-3 = 0 (x-3) (x + 1) = 0 ∵ x = 3 or x = - 1; (2) when y = 4, X & sup2; - 2x-3 = 4x & sup2; - 2x-7 = 0 ∵ △ = 4 + 7 × 4 = 32 ∵ X1 = 1 + 2 radical 2, X2 = 1-2 radical 2; (3) when y = - 5, X & sup2; - 2x-3 = - 5x & sup2; - 2x + 2 = 0, at this time, △ = 4-2 × 4 = - 4 ＜