Question

Prove that the function $f:N\to Y$ defined by $f\left(x\right)=4x+3$, where $Y=y=4x+3,xϵN$ is invertible. Also write the inverse of $f\left(x\right)$.

Answer 1

Given that $f:N\to Y$ , where $Y=y=4x+3$

Given $f\left(x\right)=4x+3=y$

So we get $f\left(x\right)=y=Y$

Therefore the function $f$ maps from $N$ to $f\left(x\right)$

So, the function $f\left(x\right)$ is invertible

We have $f\left(x\right)=4x+3=y$ $⟹x=\frac{y-3}{4}$

$⟹x=f^{-1}\left(y\right)=\frac{y-3}{4}$

$⟹f^{-1}\left(x\right)=\frac{x-3}{4}$