A function is surjective, when the range of the function is same as the co-domain.
Now, y=1−x2x2
⇒y−yx2=x2
⇒y=x2(y+1)
⇒x2=y+1y
∵x2≥0⇒y+1y≥0
⇒y∈(−∞,−1)∪[0,∞) or R−[−1,0).
∴ Range of f=A=R−[−1,0).
JEE Main 2019 — Mathematics Algebra
If the function f:R−1,−1→A defined by f(x)=1−x2x2, is surjective, then A is equal to
Held on 9 Apr 2019 · Verified 6 Jul 2026.
[0,∞)
R−−1
R−[−1,0)
R−(−1,0)
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