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

The domain of f(x)=(sqrt(x-2))/(sqrt(5-x)) is 2<= x<5

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domain of f(x)=(sqrt(x-2))/(sqrt(5-x))

domain

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

2 \leq x < 5

Interval Notation

[2, 5)

Solution steps

Find non-negative values for radicals:

2 \leq x \leq 5

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

2 \leq x < 5

f (x) = x 100 - x^{2}

f (x) = 2 x - 4

(2, 1), (9, 0)

f (x) = 4 cos (\frac{π}{3} x)

f (x) = \frac{6 x ^{2} + 1}{2 x ^{2} - 3}

What is the domain of f(x)=(sqrt(x-2))/(sqrt(5-x)) ?
The domain of f(x)=(sqrt(x-2))/(sqrt(5-x)) is 2<= x<5