Question

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

Answer 1

Pick the third statement.

Explanation: Restricting f(x)=|x−4|+6 to the positive‑slope branch means x ≥ 4, so f(x)=x+2 for x ≥ 4 and the range is y ≥ 6. The inverse has domain equal to the original range, so the inverse's domain is x ≥ 6 (and the inverse is f⁻¹(x)=x−2 with range y ≥ 4).