Verified Solution • 2025–26 Session moderate

QJEEM22Ma1e3f: JEE Main 2022 Mathematics - Class 12 JEEM22Ma1e3f Solution: If f ( x ) = { x + a , x ≤ 0

If f(x)={x+a,x≤0|x−4|,x>0 and g(x)={x+1,x<0(x−4)2+b,x≥0 are continuous on R, then (gof)(2)+(fog)(−2) is equal to :

Multiple Choice Options

  • A −10
  • B 10
  • C 8
  • D −8

Step-by-Step Verified Solution

f(x)={x+a,x≤0|x−4|,x>0 and g(x)={x+1,x<0(x−4)2+b,x≥0

∵ f(x) and g(x) are continuous on R

∴ a=4 and b=1−16=−15

then (gof)(2)+(fog)(−2)

=g(2)+f(−1)

=−11+3=−8

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