What is the domain of f(x)=(sqrt(-x+10))/(x^3) ?

The domain of f(x)=(sqrt(-x+10))/(x^3) is x<0\lor 0<x<= 10

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domain of f(x)=(sqrt(-x+10))/(x^3)

domain

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

x < 0 or 0 < x \leq 10

Interval Notation

(- \infty, 0) \cup (0, 10]

Solution steps

Find non-negative values for radicals:

x \leq 10

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq 10

f (x) = \frac{x ^{2}}{ln ( x )}

(\frac{1}{x - 7}) + (\frac{1}{x} - 9)

f (x) = 25 - 5^{x}

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

f (x) = 12 x - 2148

What is the domain of f(x)=(sqrt(-x+10))/(x^3) ?
The domain of f(x)=(sqrt(-x+10))/(x^3) is x<0\lor 0<x<= 10