What is the domain of f(z)=(z^2+16)/(z^2-3z-4) ?

The domain of f(z)=(z^2+16)/(z^2-3z-4) is z 4

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domain of f(z)=(z^2+16)/(z^2-3z-4)

domain

f (z) = \frac{z ^{2} + 16}{z ^{2} - 3 z - 4}

z < - 1 or - 1 < z < 4 or z > 4

Interval Notation

(- \infty, - 1) \cup (- 1, 4) \cup (4, \infty)

Solution steps

Find undefined (singularity) points:

z = 4, z = - 1

The function domain

z < - 1 or - 1 < z < 4 or z > 4

y = x^{4} - 4 x^{3}

y = - 5 sin (2 x - π)

\frac{ln ( x )}{x - 3}

f (x) = \frac{x - 9}{x - 64}

f (x) = 1 + 5 + 9 x

What is the domain of f(z)=(z^2+16)/(z^2-3z-4) ?
The domain of f(z)=(z^2+16)/(z^2-3z-4) is z<-1\lor-1<z<4\lor z>4