Let f : R → R be defined by f (x) = x2 + 1. Then, pre-images of 17 a

1.	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» (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.

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»

⇒ 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.