Question

Let f : R → R be defined by f (x) = x² + 1. Then, pre-images of 17 and – 3, respectively, are

(A) φ, {4, – 4} 

(B) {3, – 3}, φ

(C) {4, –4}, φ 

(D) {4, – 4, {2, – 2}

Answer 1

(C) is the correct choice 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.