Question

Show that the function $f:R\to R$ is defined by $f\left(x\right)=4x+3$ is invertible. Hence write the inverse of $f$.

Answer 1

$f:R\to R$

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

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

$4x_1+3=4x_2+3$

$x_1=x_2$

$f\left(x\right)$ is one-one

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

$y=4x+3$

$y-3=4x$

$x=\frac{y-3}{4}$

put $x$ in $f\left(x\right)$

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

$y-3+3=y$

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

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

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

$x=4y+3$

$4y=x-3$

$y=\frac{x-3}{4}$

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