What is the domain of f(x)=sqrt(x-2)-1/(sqrt(3-x)) ?

The domain of f(x)=sqrt(x-2)-1/(sqrt(3-x)) is 2<= x<3

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domain of f(x)=sqrt(x-2)-1/(sqrt(3-x))

domain

f (x) = x - 2 - \frac{1}{3 - x}

2 \leq x < 3

Interval Notation

[2, 3)

Solution steps

Find non-negative values for radicals:

2 \leq x \leq 3

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

2 \leq x < 3

What is the domain of f(x)=sqrt(x-2)-1/(sqrt(3-x)) ?
The domain of f(x)=sqrt(x-2)-1/(sqrt(3-x)) is 2<= x<3