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What is the range of the function $ln (9 - x^{2})$ $ln(9-x^2)$ ?

1 Answer

Nov 13, 2017

Range: $(- \infty, 2.197224577]$ $color(blue)((-oo,2.197224577])$ (upper value is approximate)

Explanation:

$(9 - x^{2})$ $(9-x^2)$ has a maximum value of $9$ $9$
and
since $ln(...)$ is only defined for arguments $> 0$

$color(white)("XXX")(9-x^2)$ must fall in $(0,9]$

$lim_(trarr0)ln(t)rarr-oo$ and (using a calculator) $ln(9) ~~2.197224577$

giving a range for $ln(9-x^2)$ of $(-oo,2.197224577]$

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