Mathematics

Problem

2. Check the injectivity and surjectivity of the following functions: (i)

f: \mathbf{N} \rightarrow \mathbf{N}

given by

f(x)=x^{2}

(ii)

f: \mathbf{Z} \rightarrow \mathbf{Z}

given by

f(x)=x^{2}

(iii)

f: \mathbf{R} \rightarrow \mathbf{R}

given by

f(x)=x^{2}

(iv)

f: \mathbf{N} \rightarrow \mathbf{N}

given by

f(x)=x^{3}

(v)

f: \mathbf{Z} \rightarrow \mathbf{Z}

given by

f(x)=x^{3}