Question

3. If g ={(1,1),(2,3), (3,5),(4,7)} a function from A = {1, 2, 3, 4}to B = {1,3,5,7)? If this is
given by the formula g (x) = ax + b, then find a and b.

Can anyone please solve this in a detailed manner.​

Answer 1

$\huge{\underline{\bf\red{QuestiØn} :}}$

$\sf If \: g = \{(1,1),(2,3), (3,5),(4,7) \} \: is \\ \sf a \: function \: from \: A = \{1, 2, 3, 4 \} \: to \\ \sf B = \{1,3,5,7 \} \: and \: this \: is \: given \: by \: the \\ \sf formula \: g(x) = ax + b, then \: find \: a \: and \: b.$

$\huge{\underline{\bf\blue{SolutiØn}\ :}}$

In the first element of the function, i.e.: ( 1 , 1 )

we have,

$\begin{aligned} & \qquad \ \ \ a(1) + b = 1 \\ \\ & \implies \boxed{a + b = 1} - - - - (i) \end{aligned}$

And, in the second element, i.e.: ( 2 , 3 )

we have,

$\begin{aligned} & \qquad \ \ a(2) + b = 3 \\ \\ & \implies \boxed{2a + b = 3} - - - - (ii) & & & & & & & & \end{aligned}$

On solving the two equations (i) and (ii) , we get :

• a = ( 2 )

• b = ( - 1 )

$\red{\rule{5.5cm}{0.02cm}}$

$\Large{ \mid {\underline{\underline{\bf\green{BrainLiest \ AnswEr}}}} \mid }$