The function $\mathrm{f}$ is given by $\mathrm{f}:x\mapsto {{x}^{2}}-6\lambda x,x\in \mathbb{R},$ where $\lambda $ is a positive constant. Find, in terms of $\lambda $,
<ol class="i-list"><li><div class="list-item-content">$\mathrm{ff}\left( \lambda \right)$,</div>[2]</li><li><div class="list-item-content">the range of $\mathrm{f}$.</div>[2]</li></ol>
Give a reason why $\mathrm{f}$ does not have an inverse.[1]
The function $\mathrm{f}$ 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 ${{\mathrm{f}}^{-1}}\left( x \right)$ corresponding to each of these domains for $\mathrm{f}$.[4]

The function $\mathrm{f}$ is given by $\mathrm{f}:x\mapsto {{x}^{2}}-6\lambda x,x\in \mathbb{R},$ where $\lambda $ is a positive constant. Find, in terms of $\lambda $,

Give a reason why $\mathrm{f}$ does not have an inverse.

The function $\mathrm{f}$ 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 ${{\mathrm{f}}^{-1}}\left( x \right)$ corresponding to each of these domains for $\mathrm{f}$.

Functions Revision Set Tutorial Q1

Functions Revision Set Tutorial Q1

Video Solution:

Solution:

Solution locked