Let ƒ : R → R, x ↔ x² − 4x + 7. (a) Is f injective? If not, find the largest possible set DCR such that ƒ : D → R is injective. (b) Is f surjective? If not, find the largest possible set CCR such that ƒ : R → C is surjective. (c) Is f bijective? If not, find D, C C R such that ƒ : D → C is bijective. Find the inverse function f-¹: C → D. (d) Draw the graph of both functions, f: D→ C and f-¹: C → D.
Let ƒ : R → R, x ↔ x² − 4x + 7. (a) Is f injective? If not, find the largest possible set DCR such that ƒ : D → R is injective. (b) Is f surjective? If not, find the largest possible set CCR such that ƒ : R → C is surjective. (c) Is f bijective? If not, find D, C C R such that ƒ : D → C is bijective. Find the inverse function f-¹: C → D. (d) Draw the graph of both functions, f: D→ C and f-¹: C → D.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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
Transcribed Image Text:Let ƒ : R → R, x ↔ x² − 4x + 7.
(a) Is f injective? If not, find the largest possible set DCR such that ƒ : D → R
is injective.
(b) Is f surjective? If not, find the largest possible set CCR such that ƒ : R → C
is surjective.
(c) Is f bijective? If not, find D, C C R such that ƒ : D → C is bijective. Find
the inverse function f-¹: C → D.
(d) Draw the graph of both functions, f: D→ C and f-¹: C → D.
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