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## Homework Statement

Assume f:A[tex]\rightarrow[/tex]B

g:B[tex]\rightarrow[/tex]C

h=g(f(a))=c

Give a counterexample to the following statement. If h is surjective, then f is surjective.

## Homework Equations

Definition ofSurjection: Assume f:A[tex]\rightarrow[/tex]B, For all b in B there is an a in A such that f(a)=b

## The Attempt at a Solution

f(a)=1/a from [tex]\Re[/tex] to [tex]\Re[/tex]

g(b)=1/b from [tex]\Re[/tex] to [tex]\Re[/tex]

h(a)=a from [tex]\Re[/tex] to [tex]\Re[/tex]

h is a surjection and f is not.

Does this work?