What is the domain of f(x)=sqrt(x/4-1/(x-3)) ?

The domain of f(x)=sqrt(x/4-1/(x-3)) is -1 = 4

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domain of f(x)=sqrt(x/4-1/(x-3))

domain

f (x) = \frac{x}{4} - \frac{1}{x - 3}

- 1 \leq x < 3 or x \geq 4

Interval Notation

[- 1, 3) \cup [4, \infty)

Solution steps

Find non-negative values for radicals:

- 1 \leq x < 3 or x \geq 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 1 \leq x < 3 or x \geq 4

f (x) = 10 - 3 x - x^{2}

- lo g_{4} (x)

f (x) = 2 x - 1 + 3

t

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

What is the domain of f(x)=sqrt(x/4-1/(x-3)) ?
The domain of f(x)=sqrt(x/4-1/(x-3)) is -1<= x<3\lor x>= 4