If f(x) and g(x) are two functions with g (x) = ` x - 1/x and fog (x) =x^(3) -1/x^(3) ` then f(x) is

Options

A. `3x^(2)+3`
B. `x^(2)- 1/x^(2)`
C. `1+1/(x^(2))`
D. ` 3x^(2) + 3/x^(4)`

Answer

A

Explanation

Since , `f(x-1/x) =x^(3) - 1/(x^(3)`
` f(x-1/x) = (x-1/x) (x^(2)+1/x^(2) +1)`
` = (x -1/x) [ (x-1/x)^(2) +3]`
` Rightarrow f(x) = x(x^(2)+3) =x^(3) +3x`
`[ "let" x -1/x =x]`
` Rightarrow f(x) = 3x^(2)+3`