What is the domain of (sqrt(49-x^2))/(sqrt(x^2-16)) ?

The domain of (sqrt(49-x^2))/(sqrt(x^2-16)) is -7<= x<-4\lor 4<x<= 7

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domain of (sqrt(49-x^2))/(sqrt(x^2-16))

domain

\frac{49 - x ^{2}}{x ^{2} - 16}

- 7 \leq x < - 4 or 4 < x \leq 7

Interval Notation

[- 7, - 4) \cup (4, 7]

Solution steps

Find non-negative values for radicals:

- 7 \leq x \leq - 4 or 4 \leq x \leq 7

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

- 7 \leq x < - 4 or 4 < x \leq 7

\frac{3 + 4 x}{1 - 5 x}

f (x) = \frac{2 x}{x + 1}

e^{x}

f (x) = - 9 x + 54

y = x + 2

What is the domain of (sqrt(49-x^2))/(sqrt(x^2-16)) ?
The domain of (sqrt(49-x^2))/(sqrt(x^2-16)) is -7<= x<-4\lor 4<x<= 7