What is the domain of sqrt((16x^2-49)/(x^2-64)) ?

The domain of sqrt((16x^2-49)/(x^2-64)) is x 8

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domain of sqrt((16x^2-49)/(x^2-64))

domain

x < - 8 or - \frac{7}{4} \leq x \leq \frac{7}{4} or x > 8

Interval Notation

(- \infty, - 8) \cup [- \frac{7}{4}, \frac{7}{4}] \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x < - 8 or - \frac{7}{4} \leq x \leq \frac{7}{4} or x > 8

Find undefined (singularity) points:

x = 8, x = - 8

Combine real regions and undefined points for final function domain

x < - 8 or - \frac{7}{4} \leq x \leq \frac{7}{4} or x > 8

What is the domain of sqrt((16x^2-49)/(x^2-64)) ?
The domain of sqrt((16x^2-49)/(x^2-64)) is x<-8\lor-7/4 <= x<= 7/4 \lor x>8