What is the domain of f(x)=(sqrt(2-x))/(ln(x^2)) ?

The domain of f(x)=(sqrt(2-x))/(ln(x^2)) is x<-1\lor-1<x<0\lor 0<x<1\lor 1<x<= 2

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domain of f(x)=(sqrt(2-x))/(ln(x^2))

domain

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

x < - 1 or - 1 < x < 0 or 0 < x < 1 or 1 < x \leq 2

Solution steps

Find non-negative values for radicals:

x \leq 2

Find positive values for logs:

x < 0 or x > 0

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or - 1 < x < 0 or 0 < x < 1 or 1 < x \leq 2

y = 2 tan (2 x) + 1

2^{x + 1} - 2

\frac{x - 4}{x - 2}

f (x) = ln (2 x - 6)

f (x) = x^{2} - 64

What is the domain of f(x)=(sqrt(2-x))/(ln(x^2)) ?
The domain of f(x)=(sqrt(2-x))/(ln(x^2)) is x<-1\lor-1<x<0\lor 0<x<1\lor 1<x<= 2