What is the domain of f(x)=(x+1)/(sqrt(5x^2-16)) ?

The domain of f(x)=(x+1)/(sqrt(5x^2-16)) is x 4/(sqrt(5))

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domain of f(x)=(x+1)/(sqrt(5x^2-16))

domain

f (x) = \frac{x + 1}{5 x ^{2} - 16}

x < - \frac{4}{5} or x > \frac{4}{5}

Interval Notation

(- \infty, - \frac{4}{5}) \cup (\frac{4}{5}, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - \frac{4}{5} or x \geq \frac{4}{5}

Find undefined (singularity) points:

x = \frac{4}{5}, x = - \frac{4}{5}

Combine real regions and undefined points for final function domain

x < - \frac{4}{5} or x > \frac{4}{5}

What is the domain of f(x)=(x+1)/(sqrt(5x^2-16)) ?
The domain of f(x)=(x+1)/(sqrt(5x^2-16)) is x<-4/(sqrt(5))\lor x> 4/(sqrt(5))