How do you find the domain and range of #log_(6) (49-x^2)#?

1 Answer
May 30, 2017

Answer:

The argument of a #log# function must be positive.

Explanation:

So
#49-x^2>0->x^2<49#

This only happens if
#-7 < x<+7# this is the domain

Range:
With #x# nearing #+-7# the argument #49-x^2# will be nearing #0# and the #log# itself will go to #-oo#

Or, in the language:
#lim_(x->+-7) log_6 (49-x^2)=-oo#

The top of the range is when the argument is maximal, this means when #x=0#, the max value will be:
#log_6 49=log_10 49/log_10 6~~2.172#
graph{log(49-x^2)/log(6) [-12.33, 12.99, -7.11, 5.55]}