<p>A piecewise function is given as</p>
<p style="text-align: center">${\mathrm{f}(x) = \begin{cases} 3 - x & \mathrm{for } 1 \leq x \leq 3, \\ \sqrt{4 - (x - 5)^2} & \mathrm{for } 3 &lt; x \leq 5 \end{cases}}$</p>
<p>And that&nbsp;$\mathrm{f}\left( x \right)=\mathrm{f}\left( x-4 \right)$ for all real values of $x$.</p>
<ol class="i-list"><li><div class="list-item-paragraph">Find the exact values of $\mathrm{f}\left( 8 \right)$ and $\mathrm{f}\left( -10 \right)$.<span class="inline-marks">[2]</span></div></li></ol>
<p>Another function $\mathrm{g}$ is defined as&nbsp;$\mathrm{g}\left( x \right)=\ln x$, ${{e}^{2}} &lt; x &lt; {{e}^{4}}$.</p>
<ol class="i-list" start="2"><li><div class="list-item-paragraph">Show that&nbsp;$\mathrm{fg}$ exists and find the exact range of $\mathrm{fg}$.<span class="inline-marks">[3]</span></div></li></ol>

${\mathrm{f}(x) = \begin{cases} 3 - x & \mathrm{for } 1 \leq x \leq 3, \\ \sqrt{4 - (x - 5)^2} & \mathrm{for } 3 < x \leq 5 \end{cases}}$

And that $\mathrm{f}\left( x \right)=\mathrm{f}\left( x-4 \right)$ for all real values of $x$.

Find the exact values of $\mathrm{f}\left( 8 \right)$ and $\mathrm{f}\left( -10 \right)$.

Another function $\mathrm{g}$ is defined as $\mathrm{g}\left( x \right)=\ln x$, ${{e}^{2}} < x < {{e}^{4}}$.

Show that $\mathrm{fg}$ exists and find the exact range of $\mathrm{fg}$.

Modulus Functions

Functions

H2 Math

International Baccalaureate Higher Level Mathematics

2022 HCI J1 BT Q1

2022 HCI J1 BT Q1

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