What is the domain of f(x)=sqrt((x+5)/((x-7)(x-2))) ?

The domain of f(x)=sqrt((x+5)/((x-7)(x-2))) is -5 7

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domain of f(x)=sqrt((x+5)/((x-7)(x-2)))

domain

f (x) = \frac{x + 5}{( x - 7 ) ( x - 2 )}

- 5 \leq x < 2 or x > 7

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq x < 2 or x > 7

Find undefined (singularity) points:

x = 7, x = 2

Combine real regions and undefined points for final function domain

- 5 \leq x < 2 or x > 7

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

y = 5 x - 3

\frac{x ^{2} - 4 x + 3}{x ^{2} - 1}

f (x) = \frac{x ^{2} - 16}{x ^{2} - x - 6}

arccos (3 x^{2} - 2)

What is the domain of f(x)=sqrt((x+5)/((x-7)(x-2))) ?
The domain of f(x)=sqrt((x+5)/((x-7)(x-2))) is -5<= x<2\lor x>7