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

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

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

domain

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

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq \frac{3}{2}

Find undefined (singularity) points:

x = 2, x = - 3

Combine real regions and undefined points for final function domain

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

\frac{1}{64} 4^{5 x - 23}

f (x) = arctan (e^{x})

f (x) = - x^{2} + 5 x - 4

f (x) = \frac{2 x}{3 x ^{2} - 13 x - 10}

\frac{x}{x ^{2} - 5 x + 4}

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