If f:$${1$$,$$2$$,$$3$$,…..$$}$$→$${0$$,±$$1$$,±$$2$$,….$$}$$ is defined by $$f(n)=n/2$$ if n is even −n−$$12$$ if n is odd then f−$$1($$−$$100)$$ is

Let f−$$1($$−$$100)=x$$⇒$$f(x)=$$−$$100$$⇒−$$(x$$−$$1)2=$$−$$100$$⇒$$x=201$$

Functions (XII)

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Question

If $f : {1, 2, 3, \dots . .} \to {0, \pm 1, \pm 2, \dots .}$ is defined by $f (n) = \{\begin{cases} n / 2 if n is even \\ - (\frac{n - 1}{2}) if n is odd \end{cases}$ then $f^{- 1} (- 100)$ is

Moderate

Solution

Let $f^{- 1} (- 100) = x \Rightarrow f (x) = - 100$
$\Rightarrow \frac{- (x - 1)}{2} = - 100 \Rightarrow x = 201$

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