What is the domain of f(x)=(1-3/x)^{1/(1-x)} ?

The domain of f(x)=(1-3/x)^{1/(1-x)} is x 3

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domain of f(x)=(1-3/x)^{1/(1-x)}

domain

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

x < 0 or x > 3

Interval Notation

(- \infty, 0) \cup (3, \infty)

Solution steps

Check exponents domain:

x < 0 or x > 3

Find undefined (singularity) points:

x = 0, x = 1

Combine real regions and undefined points for final function domain

x < 0 or x > 3

2 - lo g_{\frac{1}{3}} (x - 1)

- x^{2} ln (x)

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

f (x) = 3 + lo g_{3} (x + 2)

f (x) = 2 + 9 - x^{2}

What is the domain of f(x)=(1-3/x)^{1/(1-x)} ?
The domain of f(x)=(1-3/x)^{1/(1-x)} is x<0\lor x>3