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Question
Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are ______.
Options
φ, {4, – 4}
{3, – 3}, φ
{4, – 4}, φ
{4, – 4, {2, – 2}
Solution
Let f: R → R be defined by f(x) = x2 + 1. Then, pre-images of 17 and – 3, respectively, are {4, – 4}, φ.
Explanation:
Since for f–1(17) = x
⇒ f(x) = 17 or x2 + 1 = 17
⇒ x = ± 4 or f–1(17)
= {4, – 4} and for f–1(–3) = x
⇒ f(x) = – 3
⇒ x2 + 1 = – 3
⇒ x2 = – 4 and hence f–1(– 3) = φ
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