? xy ve?rsus ?yx Consider positive real num ? bers ?? and ? . Notice that . Describe the regions in the-first quadran?t of the x ? y-plane in? whi?ch x? y > ? x and .

Solution 80AE Step1 Given that Real number x and y It is true that 3 4 2 3 2 4 4 <3 , 3 >2 , 4 =2 So if x 4, y 2 Then, y x x y if x 4, y 3(>2) Then, y x x < y Also, if x 3(< 4), y 2 Step2 Then, y x x < y So, for condition of x < y is x4, y>2 So, The domain and range of first quadrant is x:[4,), y:[2,) Then, x > y x So, for condition of x > y is x<4, y2 So, The domain and range of first quadrant is x:[0,4), y:[0,2)