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GATE 2021 ES – Question 51

Mathematics Foundation · Calculus · 2 marks · Numerical answer

$f(x)+3f(g(x))=x-2$,where $g(x)=(3x+1)/(x-3)$. Find $f(5)/f(8)$ as an integer.

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Correct answer: 5 to 5

Explanation

Compute g(5)=8 and g(8)=5. Let a=f(5),b=f(8). Then a+3b=3 and b+3a=6. Solving gives a=15/8,b=3/8,so ratio a/b=**5**. Directly substituting5 alone leaves two function values, so both equations are needed.

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