What is the domain of f(x)=(x/(x+7))/(x/(x+7)+7) ?

The domain of f(x)=(x/(x+7))/(x/(x+7)+7) is x -49/8

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domain of f(x)=(x/(x+7))/(x/(x+7)+7)

domain

f (x) = \frac{\frac{x}{x + 7}}{\frac{x}{x + 7} + 7}

x < - 7 or - 7 < x < - \frac{49}{8} or x > - \frac{49}{8}

Interval Notation

(- \infty, - 7) \cup (- 7, - \frac{49}{8}) \cup (- \frac{49}{8}, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{49}{8}, x = - 7

The function domain

x < - 7 or - 7 < x < - \frac{49}{8} or x > - \frac{49}{8}

What is the domain of f(x)=(x/(x+7))/(x/(x+7)+7) ?
The domain of f(x)=(x/(x+7))/(x/(x+7)+7) is x<-7\lor-7<x<-49/8 \lor x>-49/8