Moderate -0.8 This question requires straightforward function composition and testing for odd/even properties using definitions. The compositions ln(1+x²) and 1+(ln x)² are direct substitutions, and checking odd/even involves routine algebraic verification of f(-x) vs f(x). It's simpler than average A-level questions as it requires only basic recall and application of definitions with no problem-solving or multi-step reasoning.
The functions f(x) and 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 fg(x) and gf(x), and state whether these functions are odd, even or neither. [4]
The functions f(x) and 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 fg(x) and gf(x), and state whether these functions are odd, even or neither. [4]
\hfill \mbox{\textit{OCR MEI C3 Q2 [4]}}