What is the domain of f(x)=(x^4+9x^2)/(log_{3)(2x-x^2)} ?

The domain of f(x)=(x^4+9x^2)/(log_{3)(2x-x^2)} is 0<x<1\lor 1<x<2

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domain of f(x)=(x^4+9x^2)/(log_{3)(2x-x^2)}

domain

f (x) = \frac{x ^{4} + 9 x ^{2}}{lo g _{3} ( 2 x - x ^{2} )}

0 < x < 1 or 1 < x < 2

Interval Notation

(0, 1) \cup (1, 2)

Solution steps

Find positive values for logs:

0 < x < 2

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

0 < x < 1 or 1 < x < 2

y = 10 x - 32

y = \frac{2 x + 3}{3 x + 5}

y - 5 = \frac{2}{9} (x + 6)

f (x) = \frac{x + 4}{x}

f (x) = 2 x + 2

What is the domain of f(x)=(x^4+9x^2)/(log_{3)(2x-x^2)} ?
The domain of f(x)=(x^4+9x^2)/(log_{3)(2x-x^2)} is 0<x<1\lor 1<x<2