What is the domain of f(x)=sqrt(((x+4)(x+5))/(x-7)) ?

The domain of f(x)=sqrt(((x+4)(x+5))/(x-7)) is -5 7

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domain of f(x)=sqrt(((x+4)(x+5))/(x-7))

domain

f (x) = \frac{( x + 4 ) ( x + 5 )}{x - 7}

- 5 \leq x \leq - 4 or x > 7

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq - 4 or x > 7

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

- 5 \leq x \leq - 4 or x > 7

x + 3

\frac{x}{2 + x}

(4, - 6), (6, 8)

sin (cos (tan (x)))

(- 4, - 4), (- 3, 0)

What is the domain of f(x)=sqrt(((x+4)(x+5))/(x-7)) ?
The domain of f(x)=sqrt(((x+4)(x+5))/(x-7)) is -5<= x<=-4\lor x>7