What is the domain of f(x)=sqrt(x-5)-(x+1)/(x-10) ?

The domain of f(x)=sqrt(x-5)-(x+1)/(x-10) is 5 10

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domain of f(x)=sqrt(x-5)-(x+1)/(x-10)

domain

f (x) = x - 5 - \frac{x + 1}{x - 10}

5 \leq x < 10 or x > 10

Interval Notation

[5, 10) \cup (10, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 10

Combine real regions and undefined points for final function domain

5 \leq x < 10 or x > 10

f (x) = 7^{- x}

f (x) = 3 x^{x - 2}

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

x^{3} - 125

f (x) = c + (ln (x))^{2}

What is the domain of f(x)=sqrt(x-5)-(x+1)/(x-10) ?
The domain of f(x)=sqrt(x-5)-(x+1)/(x-10) is 5<= x<10\lor x>10