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प्रश्न
If f : R → R be defined by f(x) = x2 + 1, then find f−1 [17] and f−1 [−3].
उत्तर
If f : A → B is such that y ∈ B, then \[f^{- 1}\] { y }={x ∈ A: f (x) = y}.
In other words, f -1{ y} is the set of pre - images of y.
Let
Then, f (x) =17 .
⇒ x2 +1 = 17
⇒ x2 = 17 -1 = 16
⇒ x = ± 4
∴ \[f^{- 1}\] {17} = { -4,4}
Then, f (x) =-3
⇒ x2 + 1 = -3
⇒ x2 =- 3 - 1 = -4
So
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