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JEE Main20254 Apr 2025Morning ShiftMathematicsFunctionsActual

Let f, ~g :(1, ) R be defined as f( x )= 2 x+3 5 x+2 and g(x)= 2-3 x 1-x . If the range of the function f g:[2,4] R is [ , ] , then 1 - is equal to

Options

  1. A68
  2. B29
  3. C2
  4. D56

Correct answer

D. 56

Step-by-step solution

aligned & fog (x)=f(g(x)) & =f ( 2-3 x 1-x )= 2 ( 2-3 x 1-x )+3 5 ( 2-3 x 1-x )+2 & = 4-6 x+3-3 x 10-15 x+2-2 x = ( 7-9 x 12-17 x ) & [ array c 12-7 x 0 x 12 17 array . & [ array l fog (2)= 7-9(2) 12-17(2) = -11 -22 = 1 2 fog (4)= 7-9(4) 12-17(4) = -29 -56 = 29 56 array . & Range of fog : [ , ]= [ 1 2 , 29 56 ] & ( - )= 29 56 - 1 2 = 29-28 56 = 1 56 & 1 ( - ) =56 aligned

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