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

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

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

domain

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

1 \leq x < 2

Interval Notation

[1, 2)

Solution steps

Find non-negative values for radicals:

1 \leq x \leq 2

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

1 \leq x < 2

g (x) = 4 - 4 x + x^{2}

\frac{2 x + 1}{3}

f (x) = \frac{2 x + 4}{x ^{2} + 3 x - 40}

f (x) = \frac{2 x - 7}{3 x + 5}

f (x) = \frac{2 x}{9 x - 1}

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