Question

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

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}.