Question

State the domain of f(x)=log_3(x+1)- (x^2-4)^1/2

Answer 1

Let's analyse both terms. \(\log_3(x+1)\) has a domain simply where \(x + 1 > 0\), or \(x > -1\). Similarly, \((x^2-4)^{1/2}\) has a domain where \(x^2 - 4 \ge 0\) or \((-\infty, -2] \cup [2, \infty)\).

The above two conditions have to be simultaneously fulfilled.

Answer 2

\[State the Domain for f(x)=\log_3{x+1} -\sqrt{x^2-4}\]

Answer 3

Ok, Thank You very much! :)

Answer 4

No problem! What do you get for the answer?

Answer 5

\[(-\infty, -2] U [2,\infty) \]

Answer 6

Since they both have to meet the requirement, then would that be correct?

Answer 7

Remember that \(x > -1\) also, from the log term.

Answer 8

Both requirements meaning:

First: \(x \in (-1, +\infty)\)
Second: \(x \in (-\infty,-2] \cup [2, \infty)\)

Take the "intersection" of both.