x=3 |y| -4

Question

what are the four point of this inverse

Answer 1

I assume that x=3|y|-4 is the inverse function because this function has no inverse function according to the definition of function: that is, y=f(x) requires x to map to one and only one value of y, while different values of x are permitted to map to the same y value. x=3|y|-4 maps different values of y to the same value of x.

Three important points are the x and y intercepts. When x=0, 3|y|=4, |y|=4/3, so y=4/3 or -4/3 (y-intercepts). When y=0, x=-4 so -4 is the x intercept and (-4,0) is also the vertex.

A fourth arbitrary point could be when x=y: y=3|y|-4, y+4=3|y|, squaring:

y²+8y+16=9y², 8y²-8y-16=0, y²-y-2=(y-2)(y+1). This gives us two points: (2,2) and (-1,-1).

So we have 5 points: (-4,0), (0,4/3), (0,-4/3), (2,2), (-1,-1) (choose 4 out of these).