The domain of f(x) = [sin x] cos left( frac{p | vedclass

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(D) For the function $f(x) = [\sin x] \cos \left( \frac{\pi}{[x - 1]} \right)$ to be defined,the denominator inside the cosine function must not be ze

Vedclass · Accepted Answer

$R - [1, 2)$

Vedclass · Answer

(D) For the function $f(x) = [\sin x] \cos \left( \frac{\pi}{[x - 1]} ight)$ to be defined,the denominator inside the cosine function must not be zero.Thus,$[x - 1] 
eq 0$.By the definition of the Greatest Integer Function,$[x - 1] = 0$ when $0 \leq x - 1 Adding $1$ to all parts of the inequality,we get $1 \leq x Therefore,the function is undefined for $x \in [1, 2)$.The domain of the function is all real numbers except the interval $[1, 2)$,which is written as $R - [1, 2)$.

The domain of $f(x) = [\sin x] \cos \left( \frac{\pi}{[x - 1]} \right)$ is (where $[.]$ denotes the Greatest Integer Function $G.I.F.$).

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