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Q.

The range of the function f(x)=1−x2x2+3 is

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a

-1,13

b

-1,13

c

−1,13

d

−1,13

answer is A.

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Detailed Solution

f(x)=y=1−x2x2+3⇒ yx2+3y=1−x2⇒ x2=1−3yy+1 Now x2≥0⇒1−3yy+1≥0⇒3y−1y+1≤0⇒3y-1y+1≤0⇒y+1y-13≤0 Hence, y∈(−1,1/3]

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