What is the domain of f(x)=(sqrt(x-5))/((x-7)(x+3)) ?

The domain of f(x)=(sqrt(x-5))/((x-7)(x+3)) is 5 7

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domain of f(x)=(sqrt(x-5))/((x-7)(x+3))

domain

f (x) = \frac{x - 5}{( x - 7 ) ( x + 3 )}

5 \leq x < 7 or x > 7

Interval Notation

[5, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 5

Find undefined (singularity) points:

x = 7, x = - 3

Combine real regions and undefined points for final function domain

5 \leq x < 7 or x > 7

f (x) = 2 x - 1 + x

f (x) = \frac{x ^{2} - x - 2}{x ^{4} - 81}

f (x) = - 84 x - 2

4 x - \frac{4}{3}

sin (3 x - \frac{π}{4})

What is the domain of f(x)=(sqrt(x-5))/((x-7)(x+3)) ?
The domain of f(x)=(sqrt(x-5))/((x-7)(x+3)) is 5<= x<7\lor x>7