Question

inverse of 𝑓⁡(𝑥) =𝑥 +2. Graph the function and its inverse. If necessary, restrict the domain of the inverse so that it is a function.

Answer 1

f(x) = x + 2 is one-to-one, so its inverse is a function. Solve y = x + 2 for x:

x = y − 2, so f⁻¹(x) = x − 2.

Graphs:
- f(x) = x + 2: line with slope 1, y-intercept 2 (points: (0,2), (1,3), (−2,0)).
- f⁻¹(x) = x − 2: line with slope 1, y-intercept −2 (points: (0,−2), (2,0), (3,1)).
- The two lines are reflections of each other across y = x. You can draw y = x as the mirror line to check the reflection (e.g. (0,2) on f corresponds to (2,0) on f⁻¹).

No domain restriction is necessary: domain and range of both are all real numbers.