Question

A function and its inverse are shown on the graph.



Which answer pairs a possible domain restriction for f(x) and its corresponding impact on f–1(x)?

f(x) domain: x ≥ 1
f–1(x) domain: x ≥ 1
f(x) domain: x ≥ 1
f–1(x) range: y ≥ 1
f(x) domain: x ≤ –2
f–1(x) domain: x ≤ –2
f(x) domain: x ≤ –2
f–1(x) range: y ≤ –2

Answer 1

Correct choice:
f(x) domain: x ≥ 1
f⁻¹(x) range: y ≥ 1

Reason: The domain of f becomes the range of f⁻¹ (and the range of f becomes the domain of f⁻¹), so any restriction x ≥ 1 on f’s domain shows up as y ≥ 1 for f⁻¹.