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Help me solve a subspace problem

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cbecer2003

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"S={f ε C[to,t1] | f((to+t1)/2)=0} where C[to,t1] is the set of all continuous functions which map [to,t1] into R.Is S subspace of C[to,t1]?Prove that?"

I can't solve that problem.Please can you help me?
 

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