What is the domain of f(x)=sqrt(35-2x-x^2)+1/(x^2-4) ?

The domain of f(x)=sqrt(35-2x-x^2)+1/(x^2-4) is -7<= x<-2\lor-2<x<2\lor 2<x<= 5

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domain of f(x)=sqrt(35-2x-x^2)+1/(x^2-4)

domain

f (x) = 35 - 2 x - x^{2} + \frac{1}{x ^{2} - 4}

- 7 \leq x < - 2 or - 2 < x < 2 or 2 < x \leq 5

Solution steps

Find non-negative values for radicals:

- 7 \leq x \leq 5

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

- 7 \leq x < - 2 or - 2 < x < 2 or 2 < x \leq 5

f (x) = lo g_{2 x - 1} (7 - 3 x)

\frac{x ^{3} + 2 x}{x ^{2} + 1}

f (x) = x - 5 + 5 - x

56 x^{2} + 13 x - 3

\frac{cos ( x )}{1 + sin ( x )}

What is the domain of f(x)=sqrt(35-2x-x^2)+1/(x^2-4) ?
The domain of f(x)=sqrt(35-2x-x^2)+1/(x^2-4) is -7<= x<-2\lor-2<x<2\lor 2<x<= 5