It is given that $\mathrm{f}(x)=\left\{ \begin{array}{*{35}{l}} \sqrt{1-\frac{{{x}^{2}}}{{{a}^{2}}}}

Question

It is given that $\mathrm{f}(x)=\left\{ \begin{array}{*{35}{l}} \sqrt{1-\frac{{{x}^{2}}}{{{a}^{2}}}} & \mathrm{for }-a\le x\le a, \ 0 & \mathrm{for }a and that $\mathrm{f}(x+3a)=\mathrm{f}(x)$ for all real values of $x$, where $a$ is a real constant. Sketch the graph of $y=\mathrm{f}(x)$ for $-4a\le x\le 6a$. State the range of $\mathrm{f}$. Explain whether ${{\mathrm{f}}^{-1}}$ exists for $-a\le x\le 2a$.

Accepted Answer

(ii) ${{\mathrm{R}}_{\mathrm{f}}}=\left[ 0,1 \right]$ (iii) The line $y=\frac{1}{2}$ cuts $\mathrm{f}$ twice for $-a\le x\le 2a$, thus $\mathrm{f}$ is not a one-one for $-a\le x\le 2a$. Hence ${{\mathrm{f}}^{-1}}$ doesn’t exist for $-a\le x\le 2a$.

N2013 P1 Q5 [Modified]

N2013 P1 Q5 [Modified]

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