The monotonicity of compound function is that the inside and outside increase at the same time, and the inside and outside decrease differently.

1

y=3^√(x？ -2 times)

Domain x? -2x≥0

X≤0 or x≥2

The inner layer is a quadratic function, with an upward opening and an axis of symmetry of x= 1.

A=3 The outer layer is an increasing function.

∴ The increasing interval of the whole function is

2.y=4^x-2 2^x

=(2^x)^2-2 2^x

The inner layer is the exponential function 2 x.

The outer layer is a quadratic function with an upward opening and a symmetry axis of 2 x = 1, that is, x=0.

∴

The increasing interval of the whole function is

3.y=( 1/2)^[2x/(x- 1)]

The outer layer is the exponential function a= 1/2, which decreases monotonically.

The outer layer is the fractional function 2x/(x- 1).

External monotone reduction

The whole function is monotonically increasing.

The increasing intervals are (-∞, 0) and (0,+∞).

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