數學知識交流---值域

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1.f(x) must >=0
√(4x - 3) + √(4x² + 4x - 3)>=0
√(4x - 3)>=0 Or √(14x² + 4x - 3)>=0
[3/4,infinity) Or
(-infinity,-3/2],[1/2,infinity)
So f(x)'s interval is [3/4,infinity)
2.f(x) = √(4x² + 5x - 3) - √(11- 3x)
√(4x² + 5x - 3)>=0
(-infinity,1/8(-5-sqrt73)],
[1/8(sqrt73-5),infinity)
√(11- 3x)>=0
(-infinity,11/3]
So f(x)'s interval is
(-infinity,1/8(-5-sqrt73)] and
[1/8(sqrt73-5),11/3]
3.√(13 - 4x)>=0
(-infinity,13/4]
So f(x)'s interval is (-infinity,13/4]

these questions don't need using calculus.
remark:[a,b)is a<=x<b