Mathematics 10 — Exercise 4.1 · Q9 (iii)

Full question

For the following function, state the domain and range of its inverse without calculating the inverse function.

Step-by-step solution

1. The denominator excludes x=−1. The output cannot equal 1, since x/(x+1)=1 would imply x=x+1.

2. The inverse domain equals the original range.

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

3. The inverse range equals the original domain.

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

Answer

The final answer is shown below.