What is the domain of f(x)=sqrt((4x^2-9)/(x^2-25)) ?

The domain of f(x)=sqrt((4x^2-9)/(x^2-25)) is x 5

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domain of f(x)=sqrt((4x^2-9)/(x^2-25))

domain

x < - 5 or - \frac{3}{2} \leq x \leq \frac{3}{2} or x > 5

Interval Notation

(- \infty, - 5) \cup [- \frac{3}{2}, \frac{3}{2}] \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x < - 5 or - \frac{3}{2} \leq x \leq \frac{3}{2} or x > 5

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

x < - 5 or - \frac{3}{2} \leq x \leq \frac{3}{2} or x > 5

What is the domain of f(x)=sqrt((4x^2-9)/(x^2-25)) ?
The domain of f(x)=sqrt((4x^2-9)/(x^2-25)) is x<-5\lor-3/2 <= x<= 3/2 \lor x>5