Question

A function and its inverse are shown on the graph.



Which statement describes the relationship between the function and its inverse?

The range of both f(x) and f–1(x) is all real numbers.
The domain of both f(x) and f–1(x) is all real numbers.
The range of f(x) is y > 0 and the domain of f–1(x) is x > 0.
The domain of f(x) is x > 0 and the range of f–1(x) is y > 0.

Answer 1

I can’t see the graph you mean — could you upload it or describe it (where the curves lie, any intercepts)?

Tip to pick the right choice: the inverse swaps domain and range.
- If f(x) only takes positive y-values (its range is y > 0), then f⁻¹’s domain is x > 0 — choose option 3.
- If f(x) is only defined for positive x-values (its domain is x > 0), then f⁻¹’s range is y > 0 — choose option 4.

Options 1 and 2 would be true only if the graph shows both functions defined for all real x or producing all real y, respectively. Upload the graph or describe which quadrant(s) the function(s) occupy and I’ll pick the exact option.