Question

Which of sets of functions constitute linear vector spaces with respect to the naturally defined addition...

Which of sets of functions constitute linear vector spaces with respect to the naturally defined addition and scaling? Explain.

  1. Continuous unbounded functions

  2. Discontinuous odd functions

  3. Linear-fractional functions, i.e., functions of the form f(x) = ax+bcx+d

  4. The set of functions of the form f (x) = A cot(x + φ), where A andφ are arbitrary constants.

  5. The set of functions of the form f(x)=p(x)sin(2019x)+q(x)cos(2019x), where p(x) and q(x) are polynomials.

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