Easy -1.2 This is a straightforward recall question about the hyperbolic secant function requiring only knowledge that sech x = 1/cosh x, that cosh x ≥ 1 for all real x, and therefore 0 < sech x ≤ 1. It's a single-mark multiple choice question with no calculation or problem-solving required, making it easier than average even for Further Maths.
The function g is defined by
$$g(x) = \text{sech } x \quad\quad (x \in \mathbb{R})$$
Which one of the following is the range of g?
Tick (\(\checkmark\)) one box.
[1 mark]
\(-\infty < g(x) \leq -1\) \quad \(\square\)
\(-1 \leq g(x) < 0\) \quad \(\square\)
\(0 < g(x) \leq 1\) \quad \(\square\)
\(1 \leq g(x) \leq \infty\) \quad \(\square\)
The function g is defined by
$$g(x) = \text{sech } x \quad\quad (x \in \mathbb{R})$$
Which one of the following is the range of g?
Tick ($\checkmark$) one box.
[1 mark]
$-\infty < g(x) \leq -1$ \quad $\square$
$-1 \leq g(x) < 0$ \quad $\square$
$0 < g(x) \leq 1$ \quad $\square$
$1 \leq g(x) \leq \infty$ \quad $\square$
\hfill \mbox{\textit{AQA Further Paper 2 2024 Q3 [1]}}