Define the function f: R→ R by f(x) = x5 – 1, Vx € R. a) Prove that f is onto? b) Prove that f is one-to-one? c) Explain why f-¹(x) exists? What is f-¹(x)?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.4: Definition Of Function
Problem 53E
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This is discrete MATH! NEAT HAND WRITING ONLY. Please make your answer clear enough for me to understand. 

.The definition of one-to-one function f:X → Y states that V x₁ and x₂ E X, if f(x₁) = f(x₂) then x₁ = x₂.
Write the contrapositive of the definition. (Make sure you include the quantifier!)
Transcribed Image Text:.The definition of one-to-one function f:X → Y states that V x₁ and x₂ E X, if f(x₁) = f(x₂) then x₁ = x₂. Write the contrapositive of the definition. (Make sure you include the quantifier!)
Define the function f: R→ R by f(x) = x5 - 1, Vx € R.
a) Prove that f is onto?
b) Prove that f is one-to-one?
c) Explain why f-¹(x) exists? What is f-¹(x)?
Transcribed Image Text:Define the function f: R→ R by f(x) = x5 - 1, Vx € R. a) Prove that f is onto? b) Prove that f is one-to-one? c) Explain why f-¹(x) exists? What is f-¹(x)?
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