Show that the function $f: \mathbf{N} \to \mathbf{N}$ given by $f(1)=f(2)=1$ and $f(x)=x-1$ for every $x>2$ is onto but not one-one.

> [!TLDR] > Exhibit the repeated value to disprove injectivity, then exhibit a preimage formula for every codomain element to prove surjectivity. > $f:\mathbf N\to\mathbf N$, $f(1)=f(2)=1$, $f(x)=x-1$ for $x>2$. …

Show that the function f: mathbfN → mathbfN given

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f: \mathbf{N} \to \mathbf{N}

Nagaland NbseNagaland Board of School Education 2017Subjective· 2mImportance★★★★★est

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$f(1)=f(2)=1$ gives two inputs with the same output, so f is not one-one. Every $n\i …

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Question of 99

f: \mathbf{N} \to \mathbf{N}

Nagaland NbseNagaland Board of School Education 2017Subjective· 2mImportance★★★★★est

0% · 0/99 Questions

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

$f(1)=f(2)=1$ gives two inputs with the same output, so f is not one-one. Every $n\i …

Q.Show that the function $f: \mathbf{N} \to \mathbf{N}$ given by $f(1)=f(2)=1$ and $f(x)=x-1$ for every $x>2$ is onto but not one-one.

Q.Show that the function $f: \mathbf{N} \to \mathbf{N}$ given by $f(1)=f(2)=1$ and $f(x)=x-1$ for every $x>2$ is onto but not one-one.

Q.Show that the function f:N→Nf: \mathbf{N} \to \mathbf{N}f:N→N given by f(1)=f(2)=1f(1)=f(2)=1f(1)=f(2)=1 and f(x)=x−1f(x)=x-1f(x)=x−1 for every x>2x>2x>2 is onto but not one-one.

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Q.Show that the function f:N→Nf: \mathbf{N} \to \mathbf{N}f:N→N given by f(1)=f(2)=1f(1)=f(2)=1f(1)=f(2)=1 and f(x)=x−1f(x)=x-1f(x)=x−1 for every x>2x>2x>2 is onto but not one-one.

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Q.Show that the function $f: \mathbf{N} \to \mathbf{N}$ given by $f(1)=f(2)=1$ and $f(x)=x-1$ for every $x>2$ is onto but not one-one.

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Q.Show that the function $f: \mathbf{N} \to \mathbf{N}$ given by $f(1)=f(2)=1$ and $f(x)=x-1$ for every $x>2$ is onto but not one-one.

Unlock the full solution