What is the range of the function #ln(9-x^2)#?

1 Answer
Alan P.
Nov 13, 2017

Range: #color(blue)((-oo,2.197224577])# (upper value is approximate)

Explanation:

#(9-x^2)# has a maximum value of #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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