CUET Preparation Today
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 |
$\frac{3x^2 - 5}{9x^4 - 30x^2 + 26}$ $\frac{3x^2 - 5}{9x^4 - 6x^2 + 26}$ $\frac{3x^2}{x^4 + 2x^2 - 4}$ $\frac{3x^2}{9x^4 + 30x^2 - 2}$ |
$\frac{3x^2 - 5}{9x^4 - 30x^2 + 26}$ |
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)$ $= \frac{3x^2 - 5}{(3x^2 - 5)^2 + 1} = \frac{3x^2 - 5}{9x^4 - 30x^2 + 25 + 1}$ $= \frac{3x^2 - 5}{9x^4 - 30x^2 + 26}$ |
