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

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

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

domain

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

x < 0 or x \geq 3

Interval Notation

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

Solution steps

Check exponents domain:

x < 0 or x \geq 3

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or x \geq 3

C (t) = 6 t^{2} + 500 t + 8000

cos (\frac{1}{x}) (x - 3)^{2} - 4

f (x) = - 2 x^{2} + 3 x - 5, x \geq - 6

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

f (x) = \frac{x ^{2} - 9}{x ^{2} + 2 x - 8}

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