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Dom (F) = Copom (F) Rng (#) = CoDom (P)? (a) Let ƒ : R→R_ƒ(x) = √² +5. Is this function onto its indicated codomain? Prove your answers. NO observation: √x² +5 >0 Set w=-IEIR the range of F No x Such that 1+x2 =>x²=y² but it is not in √√√₂²+5 2 Domo) (Dom (P) (b) Let f: 0, ∞)[0, ∞) f(x) = 1+2. Is this function one-to-one? Prove "Yes your answers. Let x=(1) For some x, ye [0,00) Then, => 1+x² =l+y2 → x = 1+y² By *- -1 x=y

Dom (F) = Copom (F) Rng (#) = CoDom (P)? (a) Let ƒ : R→R_ƒ(x) = √² +5. Is this function onto its indicated codomain? Prove your answers. NO observation: √x² +5 >0 Set w=-IEIR the range of F No x Such that 1+x2 =>x²=y² but it is not in √√√₂²+5 2 Domo) (Dom (P) (b) Let f: 0, ∞)[0, ∞) f(x) = 1+2. Is this function one-to-one? Prove "Yes your answers. Let x=(1) For some x, ye [0,00) Then, => 1+x² =l+y2 → x = 1+y² By *- -1 x=y

Advanced Engineering Mathematics
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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(a) Let f: R → R, f(x) = codomain? Prove your answers. = ³+1. Is this function onto its indicated 5 (b) Let f: R→ R, f(x) = |x|- 1. Is this function one-to-one? Prove your answers.
Transcribed Image Text:(a) Let f: R → R, f(x) = codomain? Prove your answers. = ³+1. Is this function onto its indicated 5 (b) Let f: R→ R, f(x) = |x|- 1. Is this function one-to-one? Prove your answers.
Domi) Copom (F) Ring()= CoDom (F)? (a) Let f: RR f(x) = √x² +5. Is this function onto its indicated codomain? Prove your answers. NO observation: √x² +5 >0 but Set w=-1 EIR the range of No x F such that (b) Let f: 0,00) DomeP) (Dom (P) 0, ∞)[0, [0, ∞) f(x) = 1. Is this function one-to-one? Prove Yes Let Fx)=(1) For some x, ye [0,00) Then. => 1+x² =l+y² ১=y your answers. 1+x2 =>x²=y² √xc² +5} *-1 1+y2² туг it is not in →>> x = Not accepted because xy=[0,00) 6Q=
Transcribed Image Text:Domi) Copom (F) Ring()= CoDom (F)? (a) Let f: RR f(x) = √x² +5. Is this function onto its indicated codomain? Prove your answers. NO observation: √x² +5 >0 but Set w=-1 EIR the range of No x F such that (b) Let f: 0,00) DomeP) (Dom (P) 0, ∞)[0, [0, ∞) f(x) = 1. Is this function one-to-one? Prove Yes Let Fx)=(1) For some x, ye [0,00) Then. => 1+x² =l+y² ১=y your answers. 1+x2 =>x²=y² √xc² +5} *-1 1+y2² туг it is not in →>> x = Not accepted because xy=[0,00) 6Q=
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