What is the domain of f(x)=sqrt(4x+12)+1/(x+2) ?

The domain of f(x)=sqrt(4x+12)+1/(x+2) is -3 -2

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domain of f(x)=sqrt(4x+12)+1/(x+2)

domain

f (x) = 4 x + 12 + \frac{1}{x + 2}

- 3 \leq x < - 2 or x > - 2

Interval Notation

[- 3, - 2) \cup (- 2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 3 \leq x < - 2 or x > - 2

f (x) = 3 (x - 4)^{2} - 8

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

f (x) = - 5 + 8 x - x^{2}

\frac{x ^{2} - 4}{x ^{2} + 6}

25 x

What is the domain of f(x)=sqrt(4x+12)+1/(x+2) ?
The domain of f(x)=sqrt(4x+12)+1/(x+2) is -3<= x<-2\lor x>-2