Question

Let f(x)=x+a/x+b such that f(f(1)=0 & f(2)=-3 then a&b resctivily are.

A, 1,-5/3 B, -5/3,3 C, 1,-3 D,none of the above​

Answer 1

The value of a = - 1 , And b =
`( - 7 )/(3)`

Explanation:

Given as :

Function f(x) =
`((x + a))/((x + b))`

And f(f(1)) = 0 And f(2) = - 3

Now For , x = 2 , y = - 3

I.e f(2) =
`((2 + a))/((2 + b))`

or, - 3 =
`((2 + a))/((2 + b))`

I.e 2 + a = - 6 - 3b

Or, a + 3b = - 8 ....... 1

Again f(f(1)) = 0

So,
`((1 + a))/((1 + b))` = 0

Or, 1 + a = 0

∴ a = - 1

So , put htis value of a i n eq 1 , we get value of b

So , - 1 + 3b = - 8

Or, 3b = - 7

∴ b =
`( - 7 )/(3)`

Hence The value of a = - 1 , And b =
`( - 7 )/(3)` Answer