What is the domain of f(x)=(x-9)/(x^2-4x-45) ?

The domain of f(x)=(x-9)/(x^2-4x-45) is x 9

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domain of f(x)=(x-9)/(x^2-4x-45)

domain

f (x) = \frac{x - 9}{x ^{2} - 4 x - 45}

x < - 5 or - 5 < x < 9 or x > 9

Interval Notation

(- \infty, - 5) \cup (- 5, 9) \cup (9, \infty)

Solution steps

Find undefined (singularity) points:

x = 9, x = - 5

The function domain

x < - 5 or - 5 < x < 9 or x > 9

ln (x^{2} - 2 x + 5)

y = 2 arcsin (x - 3) + \frac{π}{4}

f (x) = x^{5} + 12 x

y = \frac{3 x - 4}{2 x ^{2} - 1}

f (x) = 3 - lo g_{10} (1 + x^{2})

What is the domain of f(x)=(x-9)/(x^2-4x-45) ?
The domain of f(x)=(x-9)/(x^2-4x-45) is x<-5\lor-5<x<9\lor x>9