Functions Revision Set Tutorial Q1
The function $\text{f}$ is given by $\text{f}:x\mapsto {{x}^{2}}-6\lambda x,x\in \mathbb{R},$ where $\lambda $ is a positive constant. Find, in terms of $\lambda $,
(i)
$\text{ff}\left( \lambda \right)$,
[2]
(ii)
the range of $\text{f}$.
[2]
Give a reason why $\text{f}$ does not have an inverse.
[1]
The function $\text{f}$ has an inverse if its domain is restricted to $x\le k$ and also has an inverse if its domain is restricted to $x\le k$.
Find $k$ in terms of $\lambda $, and find an expression for ${{\text{f}}^{-1}}\left( x \right)$ corresponding to each of these domains for $\text{f}$.
[4]
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