1. Is the following statement true, false, or neither?

    Given an injective function $f:A \rightarrow B$, where A is the domain and B is the codomain, then $|f(A)| = |B|$, where $f(A)$ is the image of A under f.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  2. Is the following statement true, false, or neither?

    Given a surjective function $f:A \rightarrow B$, where A is the domain and B is the codomain, then $|f(A)| = |A|$, where $f(A)$ is the image of A under f.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  3. Is the following statement true, false, or neither?

    Given a surjective function $f:A \rightarrow B$, where A is the domain and B is the codomain, then $|f(A)| = |B|$, where $f(A)$ is the image of A under f.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  4. Is the following statement true, false, or neither?

    Given a bijective function $f:A \rightarrow B$, where A is the domain and B is the codomain, then $|f(A)| = |A|$, where $f(A)$ is the image of A under f.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  5. Is the following statement true, false, or neither?

    Given a bijective function $f:A \rightarrow B$, where A is the domain and B is the codomain, then $|f(A)| = |B|$, where $f(A)$ is the image of A under f.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  6. Is the following statement true, false, or neither?

    Given a bijective function $f:A \rightarrow B$, then $|A| = |B|$.

    True
    False
    Does not make sense
    I don't know yet

    What is your answer?
  7. Find the inverse of the following function, if it exists. $$ \begin{pmatrix} -3&-2&-1&0&1&2&3 \\ -1&3&1&-2&0&2&-3 \end{pmatrix} $$

  8. Find the inverse of the following function, if it exists. $$ \begin{pmatrix} 0&1 \\ 1&0 \end{pmatrix} $$

  9. Find the inverse of the following function, if it exists. $$ \begin{pmatrix} 0&1&2&3&4 \\ 4&3&1&0&1 \end{pmatrix} $$

  10. Find the inverse of the following function, if it exists. $$ f : \{ x : x^2 < 3 \} \rightarrow \{\alpha, \beta, \gamma, \delta\} $$

  11. Given $$ f := \begin{pmatrix} 0&1&2&3&4 \\ 0&4&1&2&3 \end{pmatrix},$$ $$ g := \begin{pmatrix} 0&1&2&3&4 \\ 4&1&3&0&2 \end{pmatrix},$$ find the composition f@g.

  12. Given $$ f := \begin{pmatrix} 0&1&2&3&4 \\ 0&4&1&2&3 \end{pmatrix},$$ $$ g := \begin{pmatrix} 0&1&2&3&4 \\ 4&1&3&0&2 \end{pmatrix},$$ find the composition g@f.

  13. Given $$ f := \begin{pmatrix} 0&1&2&3&4 \\ 1&0&3&2&4 \end{pmatrix},$$ $$ g := \begin{pmatrix} 0&1&2&3&4 \\ 3&2&1&4&0 \end{pmatrix},$$ find the composition f@g.

  14. Given $$ f := \begin{pmatrix} -2&-1&0&1&2 \\ 0&-2&1&2&-1 \end{pmatrix},$$ $$ g := \begin{pmatrix} 0&1&2&3&4 \\ 0&2&3&1&4 \end{pmatrix},$$ find the composition f@g.

  15. Given $$ f := \begin{pmatrix} -2&-1&0&1&2 \\ 2&0&1&4&3 \end{pmatrix},$$ $$ g := \begin{pmatrix} 0&1&2&3&4 \\ 1&2&-1&-2&0 \end{pmatrix},$$ find the composition g@f.