What is the domain of f(x)=ln(3-x)+1/(x^2-4) ?

The domain of f(x)=ln(3-x)+1/(x^2-4) is x<-2\lor-2<x<2\lor 2<x<3

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domain of f(x)=ln(3-x)+1/(x^2-4)

domain

f (x) = ln (3 - x) + \frac{1}{x ^{2} - 4}

x < - 2 or - 2 < x < 2 or 2 < x < 3

Interval Notation

(- \infty, - 2) \cup (- 2, 2) \cup (2, 3)

Solution steps

Find positive values for logs:

x < 3

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x < 2 or 2 < x < 3

f (x) = arctan (\frac{x - 1}{x + 1})

X^{2} + 4

x^{2} - 1

(0, - 3), (3, 1)

x^{2} - 6, x \leq 0

What is the domain of f(x)=ln(3-x)+1/(x^2-4) ?
The domain of f(x)=ln(3-x)+1/(x^2-4) is x<-2\lor-2<x<2\lor 2<x<3