What is the domain and range of $ln(1-x^2)$ ?

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Answer 1 · 2018-06-06T14:30:25

Domain: ${x|-1< x <1}$ or in interval notation $(-1,1)$

Range: ${y|y<=0}$ or in interval notation $(-oo, 0]$

$ln(1-x^2)$

The input to the natural log function must be greater than zero:

$1-x^2>0$

$(x-1)(x+1)>0$

$-1< x <1$

Therefore Domain is:

${x|-1< x <1}$ or in interval notation $(-1,1)$

At zero the value of this function is $ln(1) = 0$ and as $x->1$ or as $x-> -1$ the function $f(x) -> -oo$ is the range is:

${y|y<=0}$ or in interval notation $(-oo, 0]$

graph{ln(1-x^2) [-9.67, 10.33, -8.2, 1.8]}

What is the domain and range of ln(1-x^2)ln(1-x^2)?