Question 443494
find the inverse of y=6x^2-4
is the inverse a function?
..
y=6x^2-4 (original function)
To find the inverse, interchange x and y and solve for y
x=6y^2-4
x+4=6y^2
y^2=(x+4)/6
y=+-sqrt((x+4)/6) (inverse function)
y=+-((x+4)/6)^.5
see the graph of the original function and its inverse below:

{{{ graph( 300, 300, -10,10, -10, 10, 6x^2-4,((x+4)/6)^.5,-((x+4)/6)^.5) }}}

The green and blue curves make up the inverse function. As you can see, it is not a function because for each x in the domain, there are two y's. In a function, each x can have only one y-value.  Also note that the range and domain of the original function become the domain and range of the inverse. That, is they interchange.