What is the domain of f(x)= 1/(|3-x|) ?

The domain of f(x)= 1/(|3-x|) is x 3

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domain of f(x)= 1/(|3-x|)

domain

f (x) = \frac{1}{∣ 3 - x ∣}

x < 3 or x > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

Find undefined (singularity) points:

x = 3

The function domain

x < 3 or x > 3

y = 2 x - 3

f (x) = - x^{2} - 2 x - 1

\frac{x}{x ( x - 1 )}

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

f (x) = \frac{3}{5} x - 15

What is the domain of f(x)= 1/(|3-x|) ?
The domain of f(x)= 1/(|3-x|) is x<3\lor x>3