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

The domain of f(x)=sqrt(1/(x-1)+1) is x 1

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domain of f(x)=sqrt(1/(x-1)+1)

domain

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

x \leq 0 or x > 1

Solution steps

Find non-negative values for radicals:

x \leq 0 or x > 1

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

x \leq 0 or x > 1

f (x) = \frac{x ^{2} - 7 x + 12}{x ^{2} - 9}

f (x) = x^{2} - 7 x

\frac{x ^{3} + 2 x}{x}

\frac{x}{x ^{2} + 15 x + 54}

(- 6.2) (- 6.6)

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