Question

Let f = {(0, –1), (–1, 3), (2, 3), (3, 5)} be a function from Z to Z defined by f(x) = ax + b. Then, (a, b) = ___________.

Answer 1

Given: f = {(0, –1), (–1, –3), (2, 3), (3, 5)} is a function from Z to Z defined by f(x) = ax + b


f = {(0, –1), (–1, –3), (2, 3), (3, 5)} defined by f(x) = ax + b

$$\begin{gathered} f\left(0\right)=-1 \\ \Rightarrow a\left(0\right)+b=-1 \\ \Rightarrow 0+b=-1 \\ \Rightarrow b=-1...\left(1\right) \\ f\left(2\right)=3 \\ \Rightarrow a\left(2\right)+b=3 \\ \Rightarrow 2a+b=3 \\ \Rightarrow 2a-1=3\left(\mathrm{From}\left(1\right)\right) \\ \Rightarrow 2a=3+1 \\ \Rightarrow 2a=4 \\ \Rightarrow a=2...\left(2\right) \\ \mathrm{Thus}, \\ a=2\mathrm{and}b=-1 \end{gathered}$$


Hence, (a, b) = ​(2, ​–1).


Disclaimer: The function f must be equal to f = {(0, –1), (–1, –3), (2, 3), (3, 5)}.