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

The domain of f(x)=(|x-5|)/(x-5) is x 5

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domain of f(x)=(|x-5|)/(x-5)

domain

f (x) = \frac{∣ x - 5 ∣}{x - 5}

x < 5 or x > 5

Interval Notation

(- \infty, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5

The function domain

x < 5 or x > 5

f (x) = 5 x

\frac{1}{x ^{2}} - 4

f (x) = - \frac{5}{4} x - 10

f (x) = \frac{x + 3}{x ^{2} - 4 x - 21}

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

What is the domain of f(x)=(|x-5|)/(x-5) ?
The domain of f(x)=(|x-5|)/(x-5) is x<5\lor x>5