What is the domain of f(x)=sqrt((x-5)/(x-8)-4) ?

The domain of f(x)=sqrt((x-5)/(x-8)-4) is 8<x<= 9

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domain of f(x)=sqrt((x-5)/(x-8)-4)

domain

f (x) = \frac{x - 5}{x - 8} - 4

8 < x \leq 9

Interval Notation

(8, 9]

Solution steps

Find non-negative values for radicals:

8 < x \leq 9

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

8 < x \leq 9

\frac{6 x}{7 x - 1}

x - 3

e^{x + 4}

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

f (x) = 3 x + 10 - x^{2}

What is the domain of f(x)=sqrt((x-5)/(x-8)-4) ?
The domain of f(x)=sqrt((x-5)/(x-8)-4) is 8<x<= 9