Question

Consider f : R$\to$ given by f(x) = 4x + 3, Show that f is invertible and find the inverse of f.

Answer 1

$f:R\to Rbyf\left(x\right)=4x+3Let{x}_1,x_2ϵRandf\left(x_1\right)=f\left(x_2\right)\Rightarrow 4x_1+3=4x_2+3\Rightarrow x_1=x_2\Rightarrow fisone-oneLetyϵRsuchthatf\left(x\right)=y\Rightarrow 4x+3=y\Rightarrow x=\frac{y-3}{4}ϵR\therefore fisone-one\Rightarrow fisinvertibleLetf\left(x\right)=y\Rightarrow f^{-1}\left(y\right)=x4x+3=y\Rightarrow x=\frac{y-3}{4}\Rightarrow f^{-1}\left(y\right)=\frac{y-3}{4}{f}^{-1}\left(x\right)=\frac{x-3}{4}$