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

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

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

domain

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

- 5 \leq x < - 2 or x \geq 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq x < - 2 or x \geq 2

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 5 \leq x < - 2 or x \geq 2

\frac{x ^{2} - 100}{x ^{2} + x - 90}

∣ x ∣ - 2

x^{5} - 5 x

lo g_{10} (x - 4)

f (x) = \frac{1}{9.3 x - 4.3 x ^{2}}

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