Question

If f(x)=ax+b/x and f(1)=1 and f(2)=5, what is the value of A and B?

Answer 1

`\huge\boxed{a=9 ; b = -8}`

Explanation:

`f(x) = (ax+b)/(x)`

Putting x = 1

=>
`f(1) = (a(1)+b)/(1)`

Given that f(1) = 1

=>
`1 = a + b`

=>
`a+b = 1` -------------------(1)

Now,

Putting x = 2

=>
`f(2) = (a(2)+b)/(2)`

Given that f(2) = 5

=>
`5 = (2a+b)/(2)`

=>
`2a+b = 5*2`

=>
`2a+b = 10` ----------------(2)

Subtracting (2) from (1)

`a+b-(2a+b) = 1-10\\a+b-2a-b = -9\\a-2a = -9\\-a = -9\\a = 9`

For b , Put a = 9 in equation (1)

`9+b = 1\\Subtracting \ both \ sides \ by \ 9\\b = 1-9\\b = -8`