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

Answer 1

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

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]}
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Answer 2

The domain of ( \log_6(49 - x^2) ) is ( -7 \leq x \leq 7 ), and the range is all real numbers.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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