It is given that $\,\mathrm{f}(x)=\frac{1}{x-1}$. On separate diagrams, sketch the graphs of

Question

It is given that $\,\mathrm{f}(x)=\frac{1}{x-1}$. On separate diagrams, sketch the graphs of $y=\mathrm{f}\left( \left| x \right| \right)$ and $y=\left| \mathrm{f}\left( x \right) \right|$. [2] Without the use of graphing calculator, find the exact value of the constant $a$, where $0<a<1$, for which $\left| \displaystyle\int_{\text{ }-\frac{1}{2}\ }^{\text{ }\frac{1}{2}}{\text{f (}\left| x \right|)\ \mathrm{d}x} \right|=\displaystyle\int_{\text{ }0\ }^{\text{ }a}{\left| \text{f (}x) \right|\ \mathrm{d}x}$. [4]

Accepted Answer

(b)(ii) $a=\frac34$

2013 ACJC P2 Q4

2013 ACJC P2 Q4

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