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Question

Quantitative Aptitude Question on Functions

If f(x)=5x+23x−5f(x)=\frac{5x+2 }{3x-5} and g(x)=x2−2x−1g(x)=x^2-2x-1,then the value of g(f(f(3)))g(f(f(3))) is

A

2

B

13\frac{1}{3}

C

6

D

23\frac{2}{3}

Answer

2

Explanation

Solution

f(x)=5x+23x−5f(x)=\frac{5x+2 }{ 3x-5} and g(x)=x2−2x−1g(x)=x^2-2x-1
Substituting, f(3)=(5×3+2)(3×3−5)=174f(3)=\frac{(5×3+2)}{(3×3−5)}=\frac{17}{4}

f(f(3))=(5×(174)+2)(3×(174)−5)=3f(f(3))=\frac{(5×(\frac{17}{4})+2)}{(3×(\frac{17}{4})−5)}=3
g(f(f(3)))=g(3)=9−6−1=2.g(f(f(3)))=g(3)=9−6−1=2.