If `f:R to R` be defined by `f(x)=3x^(2)-5` and `g: R to R ` by `g(x)= (x)/(x^(2)+1).` Then, gof is

Options

A. `(3x^(2)-5)/(9x^(4)-30x^(2)+26)`
B. `(3x^(2)-5)/(9x^(4)-6x^(2)+26)`
C. `(3x^(2))/(x^(4)+2x^(2)-4)`
D. `(3x^(2))/(9x^(4)+30x^(2)-2)`

Answer

A

Explanation

Given that , `f(x) = 3x^(2)-5` and `g(x) = (x)/(x^(2)+1)`
`gof= g{f(x)}=g(3x^(2)-5) `
`=(3x^(2)-5)/((3x^(2)-5)^(2)+1)=(3x^(2)-5)/(9x^(4)-30x^(2)+25 +1)`
`=(3x^(2)-5)/(9x^(4)-30x^(2)+26)`