JEE Main · 2008 · 27 Apr 2008 · Offline · Sets Relations and Functions

Let

f : N \to Y

be a function defined as

f (x) = 4 x + 3

, where

Y = {y \in N : y = 4 x + 3

for some

x \in N}

. Show that

f

is invertible and its inverse is

Answer: (D)

Solution

The map

f (x) = 4 x + 3

is strictly increasing, so it is one-to-one, and since the codomain

Y

is defined to be exactly its set of outputs it is also onto; hence

f

is a bijection and has an inverse. Writing

y = 4 x + 3

and solving for

x

gives

x = \frac{y - 3}{4}

, so the inverse is

g (y) = \frac{y - 3}{4}

JEE Main · 2008 · 27 Apr 2008 · Offline · Single correct option