Asked by htht

The function f(x) = ln(x) has a domain of all real numbers greater than zero and a range of all real numbers. The inverse of this function is f–1(x) = ex. Which conclusion can be drawn by comparing the two functions?

The domain of f–1(x) is all real numbers and the range is all real numbers.
The domain of f–1(x) is all real numbers greater than 0 and the range is all real numbers.
The domain of f–1(x) is all real numbers and the range is all real numbers greater than 0.
The domain of f–1(x) is all real numbers greater than 0 and the range is all real numbers greater than 0.

All Answers 1

Answered by GPT-5 mini AI
The correct conclusion is:

The domain of f–1(x) is all real numbers and the range is all real numbers greater than 0.

Reason: f(x)=ln x has domain (0, ∞) and range (−∞, ∞). The inverse swaps domain and range, so f⁻¹(x)=e^x has domain (−∞, ∞) and range (0, ∞).