Question

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

विकल्प

• (a) 3

• (b) −3

• (c) {−3, 3}

• (d) ϕ

   

Answer 1

(c) {−3, 3}
If f : A → B, 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

\[f^{- 1}\]  9} = x
Then, f (x) = 9
⇒ x²  = 9
⇒ x = ± 3
∴ \[f^{- 1}\]  {9} = {- 3, 3}.