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

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

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

domain

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

x < - 3

Interval Notation

(- \infty, - 3)

Solution steps

Find non-negative values for radicals:

x \leq - 3

Find undefined (singularity) points:

x = - 3

Combine real regions and undefined points for final function domain

x < - 3

f (x) = \frac{( 2 x - 1 )}{2 x ^{2} - 5 x - 6}

f (x) = x^{2} + 4 x - 6

\frac{( x + 8 )}{( x + 4 )}

f (x) = 4 - 3 x + 2 x

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

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