Question

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

• A. $g\left(y\right)=\frac{y-3}{4}$
• B. $g\left(y\right)=4+\frac{y+3}{4}$
• C. $g\left(y\right)=\frac{y+3}{4}$
• D. $g\left(y\right)=log\left|\sin (x-\frac{\pi }{4})\right|+C$

Answer 1

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

$f\left(x\right)=4x+3\Rightarrow y=4x+3Theninverseoffis\Rightarrow y-3=4x\Rightarrow \frac{y-3}{4}=x\therefore x=g\left(y\right)\therefore g\left(y\right)=\frac{\left(y-3\right)}{4}$