What is the domain of y=(3x+4)/(sqrt(-2x+6)) ?

The domain of y=(3x+4)/(sqrt(-2x+6)) is x<3

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domain of y=(3x+4)/(sqrt(-2x+6))

domain

y = \frac{3 x + 4}{- 2 x + 6}

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

\frac{x ^{2} - 3 x + 2}{x ^{2} - 4}

f (x) = x^{2} + x

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

f (x) = 2 x + 2

f (x) = \frac{2 x ^{2} - 6 x + 4}{- 3 x + 5}

What is the domain of y=(3x+4)/(sqrt(-2x+6)) ?
The domain of y=(3x+4)/(sqrt(-2x+6)) is x<3