Verified Solution • 2025–26 Session moderate

QJEEM17Ma3098: JEE Main 2017 Mathematics - Class 11 JEEM17Ma3098 Solution: Let f(x) = 2 10 .x + 1 and g(x)=3 10 .x 1. If (fog) (x) = x,…

Let f(x) = 210.x + 1 and g(x)=310.x −- 1. If (fog) (x) = x, then x is equal to :

Multiple Choice Options

  • A 310−1310−2−10{{{3^{10}} - 1} \over {{3^{10}} - {2^{ - 10}}}}
  • B 210−1210−3−10{{{2^{10}} - 1} \over {{2^{10}} - {3^{ - 10}}}}
  • C 1−3−10210−3−10{{1 - {3^{ - 10}}} \over {{2^{10}} - {3^{ - 10}}}}
  • D 1−2−10310−2−10{{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}

Step-by-Step Verified Solution

(fog) (x)   =   x

⇒\Rightarrow    \,\,\, f (g(x))   =   x

⇒\Rightarrow    \,\,\, f (310. x −- 1)   =   x    [ as    g(x) = 310. x −- 1]

⇒\Rightarrow    \,\,\, 210 . (310 . x −- 1) + 1   =   x

⇒\Rightarrow    \,\,\, 310 . x −- 1 + 2 −- 10   =   x . 2 −- 10   [dividing by 210]

⇒\Rightarrow    \,\,\, 310 . x −- 2 −- 10 . x   =   1 −- 2 −- 10

⇒\Rightarrow    \,\,\, x (310 −- 2 −- 10)   =   1 −- 2 −- 10

⇒\Rightarrow    \,\,\, x = 1−2−10310−2−10{{1 - {2^{ - 10}}} \over {{3^{10}} - {2^{ - 10}}}}

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