Question

Let A = {1, 2, 3, 4, 5, 6) and B = (2, 4, 6, 8, 10, 12). If f : A → B is given by f(x) = 2x, then f^–1 as set of ordered pairs, is ___________.

Answer 1

Given: A function f : A → B defined as f(x) = 2x, where A = {1, 2, 3, 4, 5, 6} and B = {2, 4, 6, 8, 10, 12}

$$\begin{gathered} \mathrm{Since},f\left(x\right)=2x \\ \mathrm{Therefore}, \\ f=\left\{\left(1,2\right),\left(2,4\right),\left(3,6\right),\left(4,8\right),\left(5,10\right),\left(6,12\right)\right\} \\ \mathrm{Hence}, \\ {f}^{-1}=\left\{\left(2,1\right),\left(4,2\right),\left(6,3\right),\left(8,4\right),\left(10,5\right),\left(12,6\right)\right\} \end{gathered}$$


Hence, if f : A → B is given by f(x) = 2x, then f^–1 as set of ordered pairs, is $\underline{\left\{\left(2,1\right),\left(4,2\right),\left(6,3\right),\left(8,4\right),\left(10,5\right),\left(12,6\right)\right\}}.$