Let $f:N \to Y$ be a function defined as $f\left( x \right) = 4x + 3$ where $Y = \left\{ {y \in N:y = 4x + 3\;{\rm{for\;some}}\;x \in N} \right\}$ Show that f is invertible and its inverse is

$g\left( y \right) = \frac{{3y + 4}}{3}$

$g\left( y \right) = 4 + \frac{{y + 3}}{4}$

JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

f:N \to Y

be a function defined as

f\left( x \right) = 4x + 3

where

Y = \left\{ {y \in N:y = 4x + 3\;\mathrm{for\;some}\;x \in N} \right\}

Show that f is invertible and its inverse is

View answer and explanation

Correct option: A

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

Option A (

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

) is correct because it is the inverse function obtained by solving for x in the equation y = 4x + 3.