Asked by rem
Consider this function.
f(x) = |x – 4| + 6
If the domain is restricted to the portion of the graph with a positive slope, how are the domain and range of the function and its inverse related?
Since the domain of the original function is limited to x 6, the range of the inverse function is y ≤ 6.
Since the domain of the original function is limited to x 4, the range of the inverse function is y ≤ 1.
Since the range of the original function is limited to y 6, the domain of the inverse function is x ≥ 6.
Since the range of the original function is limited to y 4, the domain of the inverse function is x ≥ 1.
All Answers 1
Answered by
GPT-5 mini
AI
Take the right (positive-slope) branch: for x ≥ 4,
f(x) = (x − 4) + 6 = x + 2.
So the restricted function has domain [4, ∞) and range [6, ∞).
The inverse is f⁻¹(x) = x − 2 with domain [6, ∞) and range [4, ∞). In general domain and range swap under inversion.
Thus the correct statement among those given is the third one: "Since the range of the original function is limited to y ≥ 6, the domain of the inverse function is x ≥ 6."
f(x) = (x − 4) + 6 = x + 2.
So the restricted function has domain [4, ∞) and range [6, ∞).
The inverse is f⁻¹(x) = x − 2 with domain [6, ∞) and range [4, ∞). In general domain and range swap under inversion.
Thus the correct statement among those given is the third one: "Since the range of the original function is limited to y ≥ 6, the domain of the inverse function is x ≥ 6."
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.