Question

Express the function f : X → R given by f(x) = x³ + 1 as set of ordered pairs, where X = {−1, 0, 3, 9, 7}. [NCERT EXEMPLAR]

Answer 1

The function f : X → R is defined by f(x) = x³ + 1, where X = {−1, 0, 3, 9, 7}.

Now,

$$\begin{gathered} f\left(-1\right)={\left(-1\right)}^3+1=0 \\ f\left(0\right)=0^3+1=1 \\ f\left(3\right)=3^3+1=28 \\ f\left(7\right)=7^3+1=344 \\ f\left(9\right)=9^3+1=730 \end{gathered}$$

So, $f=\left\{\left(x,f\left(x\right)\right):x\in X\right\}=\left\{\left(-1,0\right),\left(0,1\right),\left(3,28\right),\left(7,344\right),\left(9,730\right)\right\}$