What is the domain of f(x)= 2/(5/x+2) ?

The domain of f(x)= 2/(5/x+2) is x 0

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domain of f(x)= 2/(5/x+2)

domain

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or x > 0

Interval Notation

(- \infty, - \frac{5}{2}) \cup (- \frac{5}{2}, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = - \frac{5}{2}, x = 0

The function domain

x < - \frac{5}{2} or - \frac{5}{2} < x < 0 or x > 0

What is the domain of f(x)= 2/(5/x+2) ?
The domain of f(x)= 2/(5/x+2) is x<-5/2 \lor-5/2 <x<0\lor x>0