20
QuizMultiple Choice

Comparing a Function and Its Inverse — Quiz

Question 20 • Precalculus

Consider this function. f of x is equal to start absolute value x minus 4 end absolute value plus 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?

Answer
A
Since the domain of the original function is limited to x is greater than or equal to 6 , the range of the inverse function is y is less than or equal to 6 .
B
Since the range of the original function is limited to y is greater than or equal to 6 , the domain of the inverse function is x is greater than or equal to 6 .
C
Since the domain of the original function is limited to x is greater than or equal to 4 , the range of the inverse function is y is less than or equal to 1 .
D
Since the range of the original function is limited to y is greater than or equal to 4 , the domain of the inverse function is x is greater than or equal to 1 .

Explanation

For x ≥ 4, the graph of f(x) = |x − 4| + 6 has positive slope. On this portion, the function’s outputs are y ≥ 6, so its range is [6, ∞). An inverse swaps the original function’s domain and range, making the inverse’s domain x ≥ 6. Thus, choice C is correct.

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