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Question
Answer the following:
Find whether the following function is onto or not.
f : R → R defined by f(x) = x2 + 3 for all x ∈ R
Solution
f : R → R defined by f(x) = x2 + 3 for all x ∈ R, x2 ≥ 0
∴ f(x) ≥ 3 for all x ∈ R
∴ Range = `[3, ∞)`
Clearly 0 ∈ R has no pre-image in R because x2 + 3 ≠ 0 for any x ∈ R.
∴ f is not onto.
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