मराठी

If F : Q → Q is Defined as F(X) = X2, Then F−1 (9) is Equal to (A) 3 (B) −3 (C) {−3, 3} (D) ϕ - Mathematics

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प्रश्न

If f : Q → Q is defined as f(x) = x2, then f−1 (9) is equal to

पर्याय

  • (a) 3

  • (b) −3

  • (c) {−3, 3}

  • (d) ϕ

     
MCQ

उत्तर

(c) {−3, 3}
If f : A → B, such that y ∈ B, then 

\[f^{- 1}\] { }={x ∈ Af (x) = y}.

In other words, 

\[f^{- 1}\] { y} is the set of pre-images of  y.
Let
\[f^{- 1}\]  9} = x
Then, f (x) = 9
 x2  = 9
⇒ x = ± 3
∴ \[f^{- 1}\]  {9} = {- 3, 3}.
 
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पाठ 3: Functions - Exercise 3.6 [पृष्ठ ४२]

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आरडी शर्मा Mathematics [English] Class 11
पाठ 3 Functions
Exercise 3.6 | Q 2 | पृष्ठ ४२

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