Question:
If \(f(x)=\frac{5x+2 }{3x-5}\) and \(g(x)=x^2-2x-1\),then the value of \(g(f(f(3)))\) is
If \(f(x)=\frac{5x+2 }{3x-5}\) and \(g(x)=x^2-2x-1\),then the value of \(g(f(f(3)))\) is
Updated On: Sep 26, 2024
- 2
- \(\frac{1}{3}\)
- 6
- \(\frac{2}{3}\)
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The Correct Option is A
Solution and Explanation
\(f(x)=\frac{5x+2 }{ 3x-5}\) and \(g(x)=x^2-2x-1\)
Substituting, \(f(3)=\frac{(5×3+2)}{(3×3−5)}=\frac{17}{4}\)
\(f(f(3))=\frac{(5×(\frac{17}{4})+2)}{(3×(\frac{17}{4})−5)}=3\)
\(g(f(f(3)))=g(3)=9−6−1=2.\)
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