Question

Determine the domains of the following functions in interval notation.

f(x)=log5(x^2-25)


g(x)=1/log2(3x+6)

Answer 1

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Answer 2

The domain is what values x can take such that the function still exists.

In these two cases, there are 2 conditions that can lead to an undefined result
1) The value inside the logarithm is less than or equal to 0
2) The denominator of a function is 0

For the first case, f(x), we only have to worry about the argument inside the log being greater than, but not equal or less than zero. In other words, we want to see when x^2-25 is strictly greater than 0

The second one, g(x), we want to make sure 3x+6 is greater than zero
We also want to make sure that the fraction doesn't have 0 in the denominator, which can only happen when \[\log_{2} (3x+6) = 0\] which happens when \[3x+6 = 1\]

Answer 3

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