Question

Prove that the function $f:R\to R$ defined by $f\left(x\right)=4x+3,$ is invertible and find the inverse of $f.$

Answer 1

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

Let $f\left(x_1\right)=f\left(x_2\right)$

$\Rightarrow 4x_1+3=4x_2+3$

$\Rightarrow x_1=x_2$

Thus f is one-one

To check onto

let $y=4x+3$

$\Rightarrow x=\frac{y-3}{4}$ here $y\in R$

Thus $f\left(x\right)$ is onto

Thus f is invertible

inverse of f is $=\frac{x-3}{4}=f^{-1}\left(x\right)$.