The range of function y = 10 ^ (|x-1 | - |x + 1 |) is?

The range of function y = 10 ^ (|x-1 | - |x + 1 |) is?

|The range of X-1 | - | x + 1 |, is [- 2,2], so the range of Y is [1 / 100100]

The range of the function y = 10 + cos (x - π / 4) is?
And how to get the value of y = cos2x + 1 in "0,2 π"
And what the hell is that 2K π K

If x belongs to "0,2 π", then 2x belongs to "0,4 π". Then the value of cos2x is the image of cosx after X-axis compression. That is to say, when x belongs to "0,2 π", cos2x completes two cycles. To be specific, just draw the points of x = 0.25 π, 0.5 π, 0.75 π, π, 1.25 π, 1.5 π, 1.75 π, 2 π to connect. Y = cos2x + 1 image

Given the quadratic function y = x2-4x + 5, find the range of function under the following conditions: (1) x ∈ [- 1,0]; (2) x ∈ (1,3); (3) x ∈ (4,5)]

From the meaning of the problem, y = x2-4x + 5 = (X-2) 2 + 1, about x = 2 symmetry, as shown in the figure: (1) from the graph, the function decreases on [- 1,0], then when x = 0, y = 5. When x = - 1, y = 10. That is, when x ∈ [- 1,0], y ∈ [5,10]. (2) from the graph, the function decreases on (1,2], (2,3), then x

It is known that the analytic expression of a function is y = x & # 178; - 2, and its range is [2,5]. How many such functions are there
Detailed process to answer ~ thank you

If the domain is [2, √ 7], or add one or more values in [- √ 7, - 2], or take both intervals
Note: from the value range of y = x & # 178; - 2 is [2,5], the solution is x ∈ [2, √ 7] ∪ [- √ 7, - 2], the definition field is [2, √ 7], or [- √ 7, - 2], the value range can be [2,5], and then the value in another interval can be increased or decreased arbitrarily