Let \(f:\mathbb{R}\to\mathbb{R}\) be such that \(f(x+y)=f(x)f(y)\) for all \(x,y\in\mathbb{R}\) and \(f(0)\neq0\).
Let \(g:[1,\infty)\to\mathbb{R}\) be a differentiable function such that
\[
x^2g(x)=\int_1^x\big(t^2f(t)-tg(t)\big)\,dt
\]
Then \(g(2)\) is equal to :
- \( \frac{13}{8} \)
- \( \frac{11}{16} \)
- \( \frac{15}{32} \)
- \( \frac{17}{64} \)
The Correct Option is B
Solution and Explanation
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