Answer:
The value of a = - 1 , And b = [tex]\frac{ - 7 }{3}[/tex]
Step-by-step explanation:
Given as :
Function f(x) = [tex]\frac{(x + a)}{(x + b)}[/tex]
And f(f(1)) = 0 And f(2) = - 3
Now For , x = 2 , y = - 3
I.e f(2) = [tex]\frac{(2 + a)}{(2 + b)}[/tex]
or, - 3 = [tex]\frac{(2 + a)}{(2 + b)}[/tex]
I.e 2 + a = - 6 - 3b
Or, a + 3b = - 8 ....... 1
Again f(f(1)) = 0
So, [tex]\frac{(1 + a)}{(1 + b)}[/tex] = 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 = [tex]\frac{ - 7 }{3}[/tex]
Hence The value of a = - 1 , And b = [tex]\frac{ - 7 }{3}[/tex] Answer
