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

The domain of f(x)=sqrt((2-x)/(3x^3+4x^2)) is -4/3 <x<0\lor 0<x<= 2

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

domain

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

- \frac{4}{3} < x < 0 or 0 < x \leq 2

Interval Notation

(- \frac{4}{3}, 0) \cup (0, 2]

Solution steps

Find non-negative values for radicals:

- \frac{4}{3} < x < 0 or 0 < x \leq 2

Find undefined (singularity) points:

x = 0, x = - \frac{4}{3}

Combine real regions and undefined points for final function domain

- \frac{4}{3} < x < 0 or 0 < x \leq 2

f (x) = \frac{x ^{5} + 1}{( x ^{2} - 1 ) ^{2}}

f (x) = lo g_{10} (6 x - 1)

f (x) = 7 x - 21 + \frac{x}{x - 8}

f (x) = x 4 - x

lo g_{3} (lo g_{2} (x))

What is the domain of f(x)=sqrt((2-x)/(3x^3+4x^2)) ?
The domain of f(x)=sqrt((2-x)/(3x^3+4x^2)) is -4/3 <x<0\lor 0<x<= 2