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

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

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

domain

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

x < - 2 or - 2 < x \leq 2

Interval Notation

(- \infty, - 2) \cup (- 2, 2]

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = 3, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or - 2 < x \leq 2

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