What is the domain of f(x)= x/(sqrt(4-x))-2/(x^2-5x) ?

The domain of f(x)= x/(sqrt(4-x))-2/(x^2-5x) is x<0\lor 0<x<4

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domain of f(x)= x/(sqrt(4-x))-2/(x^2-5x)

domain

f (x) = \frac{x}{4 - x} - \frac{2}{x ^{2} - 5 x}

x < 0 or 0 < x < 4

Interval Notation

(- \infty, 0) \cup (0, 4)

Solution steps

Find non-negative values for radicals:

x \leq 4

Find undefined (singularity) points:

x = 4, x = 5, x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x < 4

f (x) = lo g_{10} (3 - 2 x) + 5

f (x) = \frac{x \cdot 10 - x}{2 x - 9}

f (x) = - x - 5 + 1

x \cdot ln (x)

(1 + sin (x)) (1 + cos (x))

What is the domain of f(x)= x/(sqrt(4-x))-2/(x^2-5x) ?
The domain of f(x)= x/(sqrt(4-x))-2/(x^2-5x) is x<0\lor 0<x<4