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## Answers

**Solution:**

**Step 1:**Isolate y to -re-write the expression as function, y = f(x)

f(x) =

**Step 2:**Solve for domain.

x + 1 = 0

x - 1 = 0 - 1

x = -1

Since x + 1 is the denominator of , when -1 is substituted to denominator x + 1 ⇒ (-1) + 1 = 0.

Note that in any rational expression, denominator can not be 0, because it will render the expression 'undefined".

Therefore:

**Domain = {x/x ≠ -1)**

**= x < -1, x > -1**

**= {-2, -3, -4,...} and {0, 1, 2, 3, ...}**

**Interval Notation (⁻∞, -1) U (-1, ⁺∞)**

**Step 3:**Solve for range

Remember that the range is the combined domain of its inverse functions.

f⁻¹(x) = -1 + 1/x

f⁻¹(x) =

Find the value of denominator x:

x = 0

Again, if the denominator is equal to 0, the rational expression is undefined.

Therefore:

**Range = {y/y ≠0}**

**= y < 0, y > 0**

**= {-1, -2, -3, ...} and {1, 2, 3, ...}**

**Interval Notation: (⁻∞, 0) U (0, ⁺∞)**