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If f(x) = [x] where [x] denotes the greatest integer not exceeding x and $g (x) = \cos (π x),$ then the range of the function gof is

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${- 1, 0, 1}$

${0}$

${- 1, 1}$

${x : - 1 \leq x \leq 1}$

answer is B.

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Detailed Solution

$\begin{array}{l} f (x) = [x] a n d g (x) = \cos (π x) \\ g o f (x) = g (f (x)) = g ([x]) = \cos π (x) \\ \forall x \in R t h e n [x] = Z \\ ∴ \cos π [x] = \cos z π = - 1, 1 \\ ∴ R a n g e = {- 1, 1} \end{array}$

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