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Oliver

10-26-2013, 04:08 AM

Which of the following is the domain of the function f(x)=log_{x-2}(x^2-4)?

(A) x \neq3

(B) x>2

(C) x>2 \ and \ x \neq3

(D) x>0 \ and \ x \neq3

Thanks!;)

nicole

10-26-2013, 04:11 AM

The base of a logarithm must be greater than zero and different than one.

x-2>0 \ and \ x-2\neq 1 \Rightarrow x>2 \ and \ x\neq 3

The argument of a logarithm must be greater than zero.

x^2-4>0 \Rightarrow (x-2)(x+2) >0 \Rightarrow x<-2 \ or \ x>2

Therefore the domain of the function f is:

x>2 \ and \ x\neq 3

Therefore the correct answer is (C).;)

Oliver

10-26-2013, 04:13 AM

Thank you for your quick reply!;)

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