Let f : R - { 3 } → R - { 1 } be defined by f x = x - 2 x - 3 . Let g : R → R be given as g ( x ) = 2 x - 3 . Then, the sum of all the values of x for which f - 1 x + g - 1 x = 13 2 is equal to

Question

Let f : R - { 3 } → R - { 1 } be defined by f x = x - 2 x - 3 . Let g : R → R be given as g ( x ) = 2 x - 3 . Then, the sum of all the values of x for which f - 1 x + g - 1 x = 13 2 is equal to, 7, 2, 5, 3

MARKS App · Accepted Answer

f x = y = x - 2 x - 3 ∴ x = 3 y - 2 y - 1 ∴ f - 1 x = 3 x - 2 x - 1 & g ( x ) = y = 2 x - 3 ∴ x = y + 3 2 ∴ g - 1 x = x + 3 2 ∵ f - 1 x + g - 1 x = 13 2 3 x - 2 x - 1 + x + 3 2 = 13 2 ∴ x 2 - 5 x + 6 = 0 has roots x 1 , x 2 ∴ sum of roots x 1 + x 2 = 5

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