Moderate -0.8 This question requires only straightforward function composition and recognition of odd/even properties. The compositions ln(1+x²) and 1+(ln x)² are direct substitutions with no algebraic manipulation, and testing symmetry is a standard routine check. It's easier than average as it involves pure recall and mechanical application of definitions rather than problem-solving.
The functions \(\text{f}(x)\) and \(\text{g}(x)\) are defined as follows.
$$\text{f}(x) = \ln x, \quad x > 0$$
$$\text{g}(x) = 1 + x^2, \quad x \in \mathbb{R}$$
Write down the functions \(\text{fg}(x)\) and \(\text{gf}(x)\), and state whether these functions are odd, even or neither. [4]
The functions $\text{f}(x)$ and $\text{g}(x)$ are defined as follows.
$$\text{f}(x) = \ln x, \quad x > 0$$
$$\text{g}(x) = 1 + x^2, \quad x \in \mathbb{R}$$
Write down the functions $\text{fg}(x)$ and $\text{gf}(x)$, and state whether these functions are odd, even or neither. [4]
\hfill \mbox{\textit{OCR MEI C3 2012 Q2 [4]}}