What is the domain of sqrt((x^2+2x-15)/(x^2-7x+6)) ?

The domain of sqrt((x^2+2x-15)/(x^2-7x+6)) is x 6

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domain of sqrt((x^2+2x-15)/(x^2-7x+6))

domain

\frac{x ^{2} + 2 x - 15}{x ^{2} - 7 x + 6}

x \leq - 5 or 1 < x \leq 3 or x > 6

Interval Notation

(- \infty, - 5] \cup (1, 3] \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or 1 < x \leq 3 or x > 6

Find undefined (singularity) points:

x = 6, x = 1

Combine real regions and undefined points for final function domain

x \leq - 5 or 1 < x \leq 3 or x > 6

f (x) = 7 x - 6

\frac{- x + 1}{x + 4}

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

f (x) = x^{2} + 2 x - 8

f (x) = sin (x + a)

What is the domain of sqrt((x^2+2x-15)/(x^2-7x+6)) ?
The domain of sqrt((x^2+2x-15)/(x^2-7x+6)) is x<=-5\lor 1<x<= 3\lor x>6