Question

If f(x+1)/x = x-1/x then f(x) =?

Answer 1

Step-by-step explanation:

Correct option is

D

−

f(x)

1

If f(x)=

x+1

x−1

, then

f[f{f(x)}]=f[f(

x+1

x−1

)]

=f

⎣

⎢

⎢

⎡

x+1

x−1

+1

x+1

x−1

−1

⎦

⎥

⎥

⎤

=f

⎣

⎢

⎢

⎡

x+1

x−1+x+1

x+1

x−1−x−1

⎦

⎥

⎥

⎤

=f[−

2x

2

]=f(−

x

1

)

Now, f(−

x

1

)=

−

x

1

+1

−

x

1

−1

=

x

−1+x

x

−1−x

=−

x−1

x+1

=−

f(x)

1

∴f[f{f(x)}]=−

f(x)

1