How do you find the domain and range of log_(6) (49-x^2)log6(49−x2)?

1 Answer
MeneerNask
May 30, 2017

The argument of a loglog function must be positive.

Explanation:

So
49-x^2>0->x^2<4949−x2>0→x2<49

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

Range:
With xx nearing +-7±7 the argument 49-x^249−x2 will be nearing 00 and the loglog 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]}

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