The range of function y = √ (4-x) + log (0.5) x is Such as the title I figured it out to be - 2 to root 3 ', but it's wrong at my level | Math enthusiast | Mathematical art

The range of function y = √ (4-x) + log (0.5) x is Such as the title I figured it out to be - 2 to root 3 ', but it's wrong at my level

Let f (x) = √ (4-x); G (x) = log (0.5) x;
It is easy to judge that f and G are monotonically decreasing in the domain (0,4)
Then y is monotonically decreasing over the domain (0,4)
So the maximum value of Y is y (0) → + ∞, that is, there is no maximum value;
The minimum value is y (4) = 0 + log (0.5) 4 = - 2
The range is
[-2,+∞).

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