JEE Main2017MathematicsFunctionsActual

Let f x = 2 10 x + 1 and g x = 3 10 x - 1 . If f o g x = x , then x is equal to:

Options

A2 10 - 1 2 10 - 3 - 10
B1 - 2 - 10 3 10 - 2 - 10
C3 10 - 1 3 10 - 2 - 10
D1 - 3 - 10 2 10 - 3 - 10

Correct answer

B. 1 - 2 - 10 3 10 - 2 - 10

Step-by-step solution

Given f g x = x Where, f x = 2 10 x + 1 , g x = 3 10 x - 1 . ⇒ f 3 10 x - 1 = 2 10 3 10 x - 1 +1 ⇒ 2 10 3 10 x - 1 + 1 = x ⇒ x 6 10 - 1 = 2 10 - 1 ⇒ x = 2 10 - 1 6 10 - 1 = 2 10 - 1 2 10 ( 2 × 3 ) 10 - 1 2 10 = 1 - 2 - 10 3 10 - 2 - 10

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