Question

how to know if x=e^y and x=y^2-2 cross each other or not?

Answer 1

graph both of them in a graphing calculator using type = "x=" then graph and hit g-solv>Isect

Answer 2

mathematically how to do it

Answer 3

I'm not 100% sure how to do it mathematically sorry :(

Answer 4

if they intersect, then there exists a point (x,y) such that (x,y) is a solution to both equations.

Answer 5

so in essence, set them equal to each other and find the (x,y) value.

Answer 6

x=e^y
x=y^2-2

notice they both equal x. this makes it easier to set them equal.

e^y = y^2 - 2

from here it's a bit tricky ill explain mroe if you want