What is the domain of f(x)=ln(x)+sqrt(|x-1|-2)+cos(x) ?

The domain of f(x)=ln(x)+sqrt(|x-1|-2)+cos(x) is x>= 3

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domain of f(x)=ln(x)+sqrt(|x-1|-2)+cos(x)

domain

f (x) = ln (x) + ∣ x - 1 ∣ - 2 + cos (x)

x \geq 3

Interval Notation

[3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 1 or x \geq 3

Find positive values for logs:

x > 0

Combine real regions and undefined points for final function domain

x \geq 3

What is the domain of f(x)=ln(x)+sqrt(|x-1|-2)+cos(x) ?
The domain of f(x)=ln(x)+sqrt(|x-1|-2)+cos(x) is x>= 3