What is the domain of f(x)=(sqrt(2-x))/(x+7) ?

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

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domain of f(x)=(sqrt(2-x))/(x+7)

domain

f (x) = \frac{2 - x}{x + 7}

x < - 7 or - 7 < x \leq 2

Interval Notation

(- \infty, - 7) \cup (- 7, 2]

Solution steps

Find non-negative values for radicals:

x \leq 2

Find undefined (singularity) points:

x = - 7

Combine real regions and undefined points for final function domain

x < - 7 or - 7 < x \leq 2

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

f (x) = \frac{x - 7}{x ^{2} - 4}

3 x^{2} + 16 x - 35

f (x) = \frac{x + 1 - x}{x}

f (x) = \frac{x}{1 - 6 x}

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