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

Answer:

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

Step-by-step explanation:

$f(x) = \frac{ax+b}{x}$

Putting x = 1

=> $f(1) = \frac{a(1)+b}{1}$

Given that f(1) = 1

=> $1 = a + b$

=> $a+b = 1$  -------------------(1)

Now,

Putting x = 2

=> $f(2) = \frac{a(2)+b}{2}$

Given that f(2) = 5

=> $5 = \frac{2a+b}{2}$

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

=> $2a+b = 10$  ----------------(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)

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