What is the domain of x/(x+10)+sqrt(x^2+6x-7) ?

The domain of x/(x+10)+sqrt(x^2+6x-7) is x = 1

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domain of x/(x+10)+sqrt(x^2+6x-7)

domain

\frac{x}{x + 10} + x^{2} + 6 x - 7

x < - 10 or - 10 < x \leq - 7 or x \geq 1

Interval Notation

(- \infty, - 10) \cup (- 10, - 7] \cup [1, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 7 or x \geq 1

Find undefined (singularity) points:

x = - 10

Combine real regions and undefined points for final function domain

x < - 10 or - 10 < x \leq - 7 or x \geq 1

f (x) = (\frac{x}{4 - x ^{2}})

2 x - 5

\frac{x - 6}{x - 4}

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

\frac{7 x}{x - 5}

What is the domain of x/(x+10)+sqrt(x^2+6x-7) ?
The domain of x/(x+10)+sqrt(x^2+6x-7) is x<-10\lor-10<x<=-7\lor x>= 1