If `f(x)=(sqrt(x-1))/(x)`, what is the domain of f(x) ?

Options

A. All real numbers except for 0
B. All real numbers greater than or equal to 1
C. All real numbers less than or equal to 1
D. All real numbers greater than or equal to -1 but less than or equal to 1

Answer

B

Explanation

To be in the domain of this function, x must not be anything that makes the expression under the radical negative or that makes the denominator zero. The expression under the radical is `x-1`, and it must be nonnegative :
`x-1 ge 0`
`x ge 1`
The denominator's simply x, which then cannot be zero. It's already been established, however, that x must be greater than or equal to 1, so that's the domain.