How to graph inverse functions

Question

Hi, I need help graphing this function. Its asking to graph the function f(x)=x²-2 and to also graph the inverse of it.m

Answer 1

Let g(x) be the inverse of f(x).  

y=x²-2 

switch x and y: x=y²-2

solve for y: y=sqrt(x+2) or -sqrt(x+2)

so g(x)=+/- sqrt(x+2)  

 

NOTE: g(x) is NOT a function in x! Therefore f(x) does not have an inverse. An inverted parabola gives you a this piecewise function that is a sideways parabola, and therefore fails the vertical line test and isn't a function. 

So the graph of f(x) is going to begin with a vertex at (0,-2) and open up, and the graph of g(x) is going to begin with a vertex at (-2,0) and open to the right, but g(x) is not a function!