What is the domain of f(x)=2-(12)/(x+5),-7<= x<= 7 ?

The domain of f(x)=2-(12)/(x+5),-7<= x<= 7 is -7<= x<-5\lor-5<x<= 7

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domain of f(x)=2-(12)/(x+5),-7<= x<= 7

domain

f (x) = 2 - \frac{12}{x + 5}, - 7 \leq x \leq 7

- 7 \leq x < - 5 or - 5 < x \leq 7

Interval Notation

[- 7, - 5) \cup (- 5, 7]

Solution steps

Set the domain to the given interval

- 7 \leq x \leq 7

Find undefined (singularity) points:

x = - 5

Join undefined points with the domain:

(x < - 5 or x > - 5) and - 7 \leq x \leq 7

- 7 \leq x < - 5 or - 5 < x \leq 7

lo g_{10} (2) (x - 2)

f (x) = x^{2} - x - 1

1 + sin (x)

2 x^{3} - 3 x^{2} - 12 x + 24

f (x) = lo g_{x + 3} (- 2 x + 3)

What is the domain of f(x)=2-(12)/(x+5),-7<= x<= 7 ?
The domain of f(x)=2-(12)/(x+5),-7<= x<= 7 is -7<= x<-5\lor-5<x<= 7