Question

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

• A. $g\left(y\right)=4+\frac{y+3}{4}$
• B. $g\left(y\right)=\frac{2y-3}{4}$
• C. $g\left(y\right)=\frac{3y+4}{3}$
• D. $g\left(y\right)=\frac{y-3}{4}$

Answer 1

The correct option is D $g\left(y\right)=\frac{y-3}{4}$

Let $y=f\left(x\right)\Rightarrow x=f^{-1}\left(y\right)$ ........(A)
$\therefore y=4x+3$
$\Rightarrow 4x=y-3\Rightarrow x=\frac{y-3}{4}$
$\Rightarrow f^{-1}\left(y\right)=\frac{y-3}{4}$ .......(using A)
$\Rightarrow g\left(y\right)=\frac{y-3}{4}$