The function $\mathrm{f}$ is defined by \[\mathrm{f}(x) = \left\{ \begin{array}{ll} 2x + 1 & \text

Question

The function $\mathrm{f}$ is defined by $$\mathrm{f}(x) = \left\{ \begin{array}{ll} 2x + 1 & \text{for}\hspace{0.5em} 0 \le x < 2 \ (x - 4)^2 + 1 & \text{for}\hspace{0.5em} 2 \le x < 4. \end{array} \right.$$ It is further given that $\mathrm{f}\left( x \right)=\mathrm{f}\left( x+4 \right)$ for all real values of $x$. Find the values of $\mathrm{f}\left( 1 \right)$ and $\mathrm{f}\left( 5 \right)$. Hence, explain why $\mathrm{f}$ is not one-one.[2] Sketch the graph of $y=\mathrm{f}\left( x \right)$ for $-4\le x<8$.[3] Find the range of $\mathrm{f}$ for $-4\le x<8$.[1]

Accepted Answer

(b)(i) f is not one-one; (b)(ii) See graph; (b)(iii) Rf = [1, 5]

2014 SRJC Promo Q11

2014 SRJC Promo Q11

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