Question

given f(x)=x^2+3,x<_ 0. sketch the graph of f and it's inverse on the same cartesian plane.

Answer 1

The given function is

$f(x)=x^2+3$

Its inverse can be founded by this way

$\begin{gathered} y=x^2+3 \\ x=y^2+3 \\ x-3=y^2 \\ y^2=x-3 \\ y=-\sqrt[]{x-3} \\ f^{-1}(x)=-\sqrt[]{x-3} \end{gathered}$

Now we need to graph them with the line of symmetry y = x