Question

If f(x) =1/2x+1, x≠-1/2 then show that f(f(x))=2x+1/2x+3, provided that x≠-3/2.

*Answer ​

Answer 1

Step-by-step explanation:

Answer

Given f(x)=

2x+1

1

Replace x by f(x), we get,

f[f(x)]=

2f(x)+1

1

∴f[f(x)]=

2(

2x+1

1

)+1

1

∴f[f(x)]=

(

2x+1

2

)+1

1

∴f[f(x)]=

(

2x+1

2+2x+1

)

1

∴f[f(x)]=

2x+3

2x+1

x



=

2

−3

, as for x=

2

−3

, f(x)=

0

1

which is undefined