Verified Solution • 2025–26 Session moderate

QJEEM23Ma5925: JEE Main 2023 Mathematics - Class 11 JEEM23Ma5925 Solution: For x ∈ R , two real valued functions f ( x ) and g ( x ) are…

For x∈R, two real valued functions f(x) and g(x) are such that, g(x)=x+1 and f∘g(x)=x+3−x. Then f(0) is equal to

Multiple Choice Options

  • A 5
  • B 0
  • C −3
  • D 1

Step-by-Step Verified Solution

g(x)=x+1fog(x)=x+3−x=(x+1)2−3(x+1)+5=g2(x)−3g(x)+5⇒f(x)=x2−3x+5∴f(0)=5

But, if we consider the domain of the composite function f∘g(x)f \circ g(x) then in that case f(0)f(0) will be not defined as g(x)\mathrm{g}(\mathrm{x}) cannot be equal to zero.

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