UPSEE Solved Model Paper 7

Given :
g (x) = x -

1

x

... (i)
fog (x) = x3−

1

x3

... (ii)
We have to find f'(x)
Using concept of composition of functions, from (ii) we have
fog (x) = f [g(x)] = x3−

1

x3

⇒ f (x−

1

x

) = x3−

1

x3

[Using (i)]
⇒ f(x−

1

x

) = (x−

1

x

)(x2+

1

x2

+1)
[Using algebraic identities - 2]
⇒ f(x−

1

x

) = (x−

1

x

)((x−

1

x

)2+3)
Replacing x−

1

x

by x; we get
f (x) = x(x2+3)
= 3x+x3
Differentiating w.r.t. x ;
f' (x) = 3 + 3x2
= 3x2+3
Hence, option 'A' is correct