What is the domain of f(x)=sqrt((-2x+1)/(x^2+x-6)) ?

The domain of f(x)=sqrt((-2x+1)/(x^2+x-6)) is x<-3\lor 1/2 <= x<2

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domain of f(x)=sqrt((-2x+1)/(x^2+x-6))

domain

f (x) = \frac{- 2 x + 1}{x ^{2} + x - 6}

x < - 3 or \frac{1}{2} \leq x < 2

Interval Notation

(- \infty, - 3) \cup [\frac{1}{2}, 2)

Solution steps

Find non-negative values for radicals:

x < - 3 or \frac{1}{2} \leq x < 2

Find undefined (singularity) points:

x = 2, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or \frac{1}{2} \leq x < 2

f (x) = \frac{5 x}{x - 9}

(- 5, - 7), (2, - 4)

f (x) = 15 x - 10

f (x) = x^{7}

y = 2 x - 1

What is the domain of f(x)=sqrt((-2x+1)/(x^2+x-6)) ?
The domain of f(x)=sqrt((-2x+1)/(x^2+x-6)) is x<-3\lor 1/2 <= x<2