Question

let A={-2,-1,0,1,0} and f:A->Z be a function defined by f(x)=x² - 2x - 3. find a. range of f and b.pre-images of 6, -3, 5

Answer 1

$$\begin{gathered} \mathrm{A}=\left\{-2,-1,0,1,2\right\} \\ \mathrm{f}\left(\mathrm{x}\right)={\mathrm{x}}^2-2\mathrm{x}-3 \\ \mathrm{f}\left(-2\right)={\left(-2\right)}^2-2\left(-2\right)-3=4+4-3=5 \\ \mathrm{f}\left(-1\right)={\left(-1\right)}^2-2\left(-1\right)-3=1+2-3=0 \\ \mathrm{f}\left(0\right)=0-0-3=-3 \\ \mathrm{f}\left(1\right)={\left(1\right)}^2-2\left(1\right)-3=1-2-3=-4 \\ \mathrm{f}\left(2\right)={\left(2\right)}^2-2\left(2\right)-3=4-4-3=-3 \\ \mathrm{Range}=\left\{-4,-3,0,5\right\} \\ \mathrm{There}\mathrm{is}\mathrm{no}\mathrm{preimage}\mathrm{of}6. \\ \mathrm{Preimages}\mathrm{of}-3\mathrm{are}0\mathrm{and}2. \\ \mathrm{Preimage}\mathrm{of}5\mathrm{is}-2. \end{gathered}$$