Find the range of the internal function t=log( 1/2)x first, because it is a monotone function.

So just substitute x = 2,4 to get t=- 1, -2 r so-2.

To find the range of the external function, the symmetry axis of y = t 2-t/2+5 is t = 1/4, and 1/4 is not within [-2,-1].

So it is monotonically decreasing. Substitute T =-2 and-1 respectively to get Y = 10 and 13/2.

So the maximum value is 10, and the minimum value is 13/2.

Reference materials;

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