If 2 g ( x ) + 3 g ( 1 x ) = x − 1 , then find the value of g(2). Options: A . &nbsp−710 B . &nbsp1210 C . &nbsp711 D . &nbsp12 E . &nbsp3q+ r

Answer: Option A : A Shortcut: Direct substitution First put x=2 2 g ( 2 ) + 3 g ( 1 2 ) = 2 − 1 = 1 Put, x = 1 2 2 g ( 1 2 ) + 3 g ( 2 ) = 1 2 − 1 = − 1 2 Solving (1) and (2), g ( 2 ) = − 7 10

If 2g(x)+3g(1x)=x−1, then find the value of g(2).

Question

2 g (x) + 3 g (\frac{1}{x}) = x - 1

, then find the value of g(2).

Answer: Option A
:
A
Shortcut: Direct substitution
First put x=2

2 g (2) + 3 g (\frac{1}{2}) = 2 - 1 = 1

Put,

x = \frac{1}{2}

2 g (\frac{1}{2}) + 3 g (2) = \frac{1}{2} - 1 = - \frac{1}{2}

Solving (1) and (2),

g (2) = - \frac{7}{10}

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