 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2022/paper-1/3/solution

The domain excludes

x = 0

. Rearranging the inequality gives

\frac{x + 1}{x} \geq 0.

A sign check on the intervals separated by

- 1

and

0

shows that the ratio is nonnegative when

x \leq - 1

x > 0

. The point

- 1

is allowed because it makes the numerator zero. Therefore

x \in (- \infty, - 1] \cup (0, \infty) .

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