f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X→V is injective. ) gof: X→ V is surjective. ) (gof)-¹ = f¹og-¹

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
Author:David Poole
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Chapter6: Vector Spaces
Section6.5: The Kernel And Range Of A Linear Transformation
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f: X→ Y and g: Y→V be bijective functions. Show the following:
) gof: X → V is injective.
) gof: X → V is surjective.
) (gof)-¹=f-¹og=¹
Use:
v injective if x1 ‡xn → v(x1) = v(xn)
Transcribed Image Text:f: X→ Y and g: Y→V be bijective functions. Show the following: ) gof: X → V is injective. ) gof: X → V is surjective. ) (gof)-¹=f-¹og=¹ Use: v injective if x1 ‡xn → v(x1) = v(xn)
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