If f - 1- 2- 3- - -0- - 1- - 2- - is defined by fn- n2- if n is even - n-12 - if n is odd then f-1-100 is

The correct option is C 201 Let n=201 . ∴ f(n)= f(201) = (201 1/2)= 100 ⇒ f^ 1( 100)=201 ...

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Properties of Inverse Function

If f : 1, 2...

Question

If $f : {1, 2, 3, . . . . . . . . .}$ $\to {0, \pm 1, \pm 2, . . . . . . .}$ is defined by
$f (n) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{n}{2}, if n is even - (\frac{n - 1}{2}), if n is odd \end{matrix}$

then $f^{- 1} (- 100)$ is

100

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199

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201

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200

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Similar questions

f : {1, 2, 3, . . . . .} \to {0, \pm 1, \pm 2, . . . . .}

f (n) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{n}{2} & if n i s e v e n - (\frac{n - 1}{2}) & if n i s o d d \end{matrix}

f^{- 1} (- 100)

Let $f : N \to N$ be defined by $f (n) = {\begin{matrix} \frac{n + 1}{2}, if n is odd \frac{n}{2}, if n is even \end{matrix}}$ for all $n \in N$ .

State whether the function $f$ is bijective. Justify your answer.

f : {1, 2, 3, . . .} \to {0, \pm 1, \pm 2, . . .}

y = f (x) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{x}{2} if x is even - \frac{(x - 1)}{2}, if x is odd \end{matrix}

f^{- 1} (100)

N \to N

f (n) = ⎧ ⎪ ⎪ ⎨ ⎪ ⎪ ⎩ \begin{matrix} \frac{n + 1}{2} & if n is odd \frac{n}{2} & if n is even \end{matrix}

f

f : W \to W

f (n) = {\begin{matrix} n-1, if n is odd n+1, if n is even \end{matrix}

f

f

W

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