Let P(R) be the vector space of all polynomial over the field R. Define T:PR)PR) by...

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Let P(R) be the vector space of all polynomial over the field R. Define T:PR)→PR) by T(f(x)) = f(t) dt. Then T'is one-one and onto Tis one-one but not onto Tis onto but not one-one Tis neither one-one nor onto Let P(R) be the vector space of all polynomial over the field R. Define T:PR)→PR) by T(f(x)) = f(t) dt. Then T'is one-one and onto Tis one-one but not onto Tis onto but not one-one Tis neither one-one nor onto

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