What is the domain of f(x)=(5^{1/x})/((x+1)^2) ?

The domain of f(x)=(5^{1/x})/((x+1)^2) is x 0

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domain of f(x)=(5^{1/x})/((x+1)^2)

domain

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

x < - 1 or - 1 < x < 0 or x > 0

Interval Notation

(- \infty, - 1) \cup (- 1, 0) \cup (0, \infty)

Solution steps

Find undefined (singularity) points:

x = - 1, x = 0

The function domain

x < - 1 or - 1 < x < 0 or x > 0

\frac{x}{6 - x}

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

(0, 1), (10, - 9)

- 8 x + 2

f (x) = \frac{5 x + 5}{8 x + 32}

What is the domain of f(x)=(5^{1/x})/((x+1)^2) ?
The domain of f(x)=(5^{1/x})/((x+1)^2) is x<-1\lor-1<x<0\lor x>0