What is the domain of f(x)=(e^{sqrt(1-2x)})/(x^2-9) ?

The domain of f(x)=(e^{sqrt(1-2x)})/(x^2-9) is x<-3\lor-3<x<= 1/2

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domain of f(x)=(e^{sqrt(1-2x)})/(x^2-9)

domain

f (x) = \frac{e ^{1 - 2 x}}{x ^{2} - 9}

x < - 3 or - 3 < x \leq \frac{1}{2}

Interval Notation

(- \infty, - 3) \cup (- 3, \frac{1}{2}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{1}{2}

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or - 3 < x \leq \frac{1}{2}

f (x) = x^{3} - 9 x^{2} + 15

f (x) = 2 x^{3} - 39 x^{2} + 240 x + 8

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

f (x) = - (\frac{1}{3})^{x} + 2

f (x) = 3^{x} - 1

What is the domain of f(x)=(e^{sqrt(1-2x)})/(x^2-9) ?
The domain of f(x)=(e^{sqrt(1-2x)})/(x^2-9) is x<-3\lor-3<x<= 1/2