What is the domain of f(x)=(3x-4)/(sqrt(x^2+4x-77)) ?

The domain of f(x)=(3x-4)/(sqrt(x^2+4x-77)) is x 7

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domain of f(x)=(3x-4)/(sqrt(x^2+4x-77))

domain

f (x) = \frac{3 x - 4}{x ^{2} + 4 x - 77}

x < - 11 or x > 7

Interval Notation

(- \infty, - 11) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 11 or x \geq 7

Find undefined (singularity) points:

x = 7, x = - 11

Combine real regions and undefined points for final function domain

x < - 11 or x > 7

What is the domain of f(x)=(3x-4)/(sqrt(x^2+4x-77)) ?
The domain of f(x)=(3x-4)/(sqrt(x^2+4x-77)) is x<-11\lor x>7