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Question

Range of the expression f(x)=x21x2+1, xR is

A
[1,1]
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B
[1,1)
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C
(1,1)
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D
(1,1]
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Solution

The correct option is B [1,1)
Let
y=x21x2+1(y1)x2+(y+1)=0
y1 because coefficient of x2 can not be 0.
xRΔ04(y1)(y+1)0(y21)0
y[1,1]
Range of y=[1,1)

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