What is the domain of f(x)=cos(1/x)+log_{10}(x+1) ?

The domain of f(x)=cos(1/x)+log_{10}(x+1) is -1 0

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domain of f(x)=cos(1/x)+log_{10}(x+1)

domain

f (x) = cos (\frac{1}{x}) + lo g_{10} (x + 1)

- 1 < x < 0 or x > 0

Interval Notation

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

Solution steps

Find positive values for logs:

x > - 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 1 < x < 0 or x > 0

What is the domain of f(x)=cos(1/x)+log_{10}(x+1) ?
The domain of f(x)=cos(1/x)+log_{10}(x+1) is -1<x<0\lor x>0