JEE Mains · Maths · STD 12 - 1. relation and function
If \(g(x)=3x^{2}+2x-3,\) \(f(0)=-3\) and \(4g(f(x))=3x^{2}-32x+72,\) then \(f(g(2))\) is equal to:
- A \(\frac{25}{6}\)
- B \(-\frac{25}{6}\)
- C \(\frac{7}{2}\)
- D \(-\frac{7}{2}\)
Answer & Solution
Correct Answer
(C) \(\frac{7}{2}\)
Step-by-step Solution
Detailed explanation
\(g(2)=13\) \(f(g(2))=f(13)\) Now \(4g(f(x))=3x^{2}-32x+72\) \(4[3f^{2}(x)+2f(x)-3]=3x^{2}-32x+72\) Let \(f(x)=t\) \(12t^{2}+8t-(3x^{2}-32x+84)=0\) \(f(x)=\frac{-8\pm\sqrt{64+48(3x^{2}-32x+84)}}{24}\) \(f(x)=\frac{-8\pm4(3x-16)}{24}\) \(\because f(0)=-3 \quad \therefore\) we…
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