Verified Solution • 2025–26 Session moderate

QJEEM08Maa777: JEE Main 2008 Mathematics - Class 11 JEEM08Maa777 Solution: Let be a function defined as f(x) = 4x + 3 where Y = { y N, y = …

Let f:N→Yf:N \to Y be a function defined as f(x) = 4x + 3 where
Y = { y ∈\in N, y = 4x + 3 for some x ∈\in N }.
Show that f is invertible and its inverse is

Multiple Choice Options

  • A g(y)=3y+44g\left( y \right) = {{3y + 4} \over 4}
  • B g(y)=4+y+34g\left( y \right) = 4 + {{y + 3} \over 4}
  • C g(y)=y+34g\left( y \right) = {{y + 3} \over 4}
  • D g(y)=y−34g\left( y \right) = {{y - 3} \over 4}

Step-by-Step Verified Solution

Clearly ff is one one and onto, so invertible

Also f(x)=4x+3=y⇒x=y−34f\left( x \right) = 4x + 3 = y \Rightarrow x = {{y - 3} \over 4}

∴\therefore     g(y)=y−34\,\,\,\,g\left( y \right) = {{y - 3} \over 4}

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