What is the domain of g(x)= 4/(ln(\frac{x^2){4})} ?

The domain of g(x)= 4/(ln(\frac{x^2){4})} is x 2

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domain of g(x)= 4/(ln(\frac{x^2){4})}

domain

g (x) = \frac{4}{ln ( \frac{x ^{2}}{4} )}

x < - 2 or - 2 < x < 0 or 0 < x < 2 or x > 2

Interval Notation

(- \infty, - 2) \cup (- 2, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find positive values for logs:

x < 0 or x > 0

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x < 0 or 0 < x < 2 or x > 2

f (x) = lo g_{10} (1 - 2 x)

f (x) = \frac{- 2 x}{x ^{4} - 72 x ^{2} + 1296}

f (x) = 2 + 26

\frac{- 2}{x - 2} - 2

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

What is the domain of g(x)= 4/(ln(\frac{x^2){4})} ?
The domain of g(x)= 4/(ln(\frac{x^2){4})} is x<-2\lor-2<x<0\lor 0<x<2\lor x>2