Q. The figure shows the graph of a function f(x) which is a semi circle centred at origin


(a) Write the domain and range of f(x)
(b) Define the function f(x)

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{On} \mathrm{x}-\mathrm{axis}, \mathrm{we} \mathrm{have} \mathrm{graph} \mathrm{from} \mathrm{x}=-4 \mathrm{to} \mathrm{x}=4, \mathrm{hence} \\ \mathrm{Domain} \mathrm{is} \mathrm{x}\in \left[-4,4\right] \\ \mathrm{Now} \\ \mathrm{Now} \mathrm{radius} \mathrm{of} \mathrm{semi}-\mathrm{circle} \mathrm{is} 4 \mathrm{units} \mathrm{and} \mathrm{origin} \mathrm{is} \mathrm{center}, \mathrm{henc} \\ \mathrm{f}\left(\mathrm{x}\right)=\sqrt{4^2-{\mathrm{x}}^2} \\ \Rightarrow \mathrm{f}\left(\mathrm{x}\right)=\sqrt{16-{\mathrm{x}}^2} \end{gathered}$$

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