Easy -1.8 This is a straightforward 1-mark multiple choice question requiring only the basic procedure for finding an inverse function (swap x and y, then solve for y). The algebra is trivial: x = e^y + 1 gives e^y = x - 1, so y = ln(x-1). No problem-solving or insight needed, just routine application of a standard technique.
The function f is defined by \(f(x) = e^x + 1\) for \(x \in \mathbb{R}\)
Find an expression for \(f^{-1}(x)\)
Tick \((\checkmark)\) one box.
[1 mark]
\(f^{-1}(x) = \ln(x - 1)\) \(\square\)
\(f^{-1}(x) = \ln(x) - 1\) \(\square\)
\(f^{-1}(x) = \frac{1}{e^x + 1}\) \(\square\)
\(f^{-1}(x) = \frac{x - 1}{e}\) \(\square\)
Question 2:
2 | Ticks the 1st box | 1.1b | B1 | f − 1 ( x ) = l n ( x − 1 )
Question 2 Total | 1
Q | Marking instructions | AO | Marks | Typical solution