If $f : R \to R$ be defined by $f(x) = 3x^2 - 5$ and $g : R \to R$ by $g(x) = \frac{x}{x^2 + 1}$. Then, $gof$ is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $\frac{3x^2 - 5}{9x^4 - 30x^2 + 26}$ ##
Given that, $f(x) = 3x^2 - 5$ and $g(x) = \frac{x}{x^2 + 1}$
$ g of = g(f(x)) = g(3x^2 - 5)$
$= \frac{3x^2 - 5}{(3x^2 - 5)^2 + 1} = \frac{3x^2 - 5}{9x^4 - 30x^2 + 25 + 1}$
$= \frac{3x^2 - 5}{9x^4 - 30x^2 + 26}$