SOLUTION: find the domain of the function. f(x)= ln(x^2-9 / x^2+9x+14)

Question 1001695: find the domain of the function.

f(x)= ln(x^2-9 / x^2+9x+14)
Answer by ikleyn(52803) (Show Source): You can put this solution on YOUR website!
.
You need to determine where the function under the logarithm,

f(x) = is greater than zero, f(x) > 0.

Notice that 1) = (x+3)*(x-3), and 2) = (x+2)*(x+7). Therefore,

f(x) = .

Now, f(x) > 0

1) in the semi-infinite interval x < -7, or (, );

2) in the interval -3 < x < -2, or (-3, -2);

3) in the semi-infinite interval x > 3, or (, ).

See the plots below.

Figure. Plot f(x) (red line);
plot of the numerator (green line);
plot of denominator (blue line).

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