If () + ( − ) = + for all real , find ()
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Step-by-step explanation:
First let us find the range where Min (-(x – 1)2 + 2, (x – 2)2 + 1) is – (x – 1)2 + 2.
In other words, in which range is – (x – 1)2 + 2 < (x – 2)2 + 1.
–(x2 – 2x +1) + 2 < x2 – 4x + 4 + 1
0 < 2x2 – 6x + 4
x2 – 3x + 2 > 0
(x – 1) (x – 2) > 0
=> x > 2 or x < 1
Answered by
2
First let us find the range where Min (-(x – 1)2 + 2, (x – 2)2 + 1) is – (x – 1)2 + 2.
In other words, in which range is – (x – 1)2 + 2 < (x – 2)2 + 1.
–(x2 – 2x +1) + 2 < x2 – 4x + 4 + 1
0 < 2x2 – 6x + 4
x2 – 3x + 2 > 0
(x – 1) (x – 2) > 0
=> x > 2 or x < 1
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