What is the domain of f(x)=(cos(1/x))/(1+1/x) ?

The domain of f(x)=(cos(1/x))/(1+1/x) is x 0

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domain of f(x)=(cos(1/x))/(1+1/x)

domain

f (x) = \frac{cos ( \frac{1}{x} )}{1 + \frac{1}{x}}

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{4 x - 8}{( x - 4 ) ( x + 1 )}

\frac{x ^{2} - 36}{x - 6}

7 x - y = - 7

f (x) = 6 x^{2} + 1

f (x) = - 3 (x + 2)^{2} + 5

What is the domain of f(x)=(cos(1/x))/(1+1/x) ?
The domain of f(x)=(cos(1/x))/(1+1/x) is x<-1\lor-1<x<0\lor x>0