What is the domain of f(x)=sqrt((2x+6)/(3x+2)) ?

The domain of f(x)=sqrt((2x+6)/(3x+2)) is x -2/3

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domain of f(x)=sqrt((2x+6)/(3x+2))

domain

f (x) = \frac{2 x + 6}{3 x + 2}

x \leq - 3 or x > - \frac{2}{3}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - 3 or x > - \frac{2}{3}

Find undefined (singularity) points:

x = - \frac{2}{3}

Combine real regions and undefined points for final function domain

x \leq - 3 or x > - \frac{2}{3}

f (x) = x (5 - 2 x) (10 - 2 x)

f (x) = lo g_{3} (x) + 2

f (x) = \frac{x + 7}{x - 2}

f (x) = \frac{- x ^{2} + 7 x - 10}{x - 3}

g (x) = \frac{1}{x - 2}

What is the domain of f(x)=sqrt((2x+6)/(3x+2)) ?
The domain of f(x)=sqrt((2x+6)/(3x+2)) is x<=-3\lor x>-2/3