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Question #7619b

1 Answer

Jul 20, 2017

$(- \infty, 0)$ $(-oo,0)$

Explanation:

Range of $x - ⌊ x ⌋$ $x - floor(x)$ is $[0, 1)$ $[0,1)$

$0$ $0$ is not in the domain of $ln$ $ln$ , and as $x$ $x$ gets close to $0$ $0$ , $ln x$ $lnx$ decreases without bound (goes to $- \infty$ $-oo$ ).

$ln 1 = 0$ $ln1 = 0$ , but $x - ⌊ x ⌋$ $x - floor(x)$ never takes on the value $1$ $1$ , so

the range of $ln (x - ⌊ x ⌋)$ $ln(x-floor(x))$ is $(- \infty, 0)$ $(-oo,0)$

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