# Inverting function variables

The original equation is a function of x. However, I want to invert the function and get an expression of x in terms of y.

Solve[y == (a x + b)/Exp[x^2], x]
InverseFunction[y == (a x + b)/Exp[x^2], x]


I've tried Solve and InverseFunction, but they both turned out to be futile.

• e should be E,or e^x^2 should be Exp[x^2] Mar 21, 2022 at 7:49
• I edited the code. Still, it doesn't work Mar 21, 2022 at 8:40
• Did you read the error message? This system cannot be solved with the methods available to Solve. Mar 21, 2022 at 8:44
• One reason InverseFunction doesn't work is because your function is not invertible. For example, for a=1, you can plot it to see Plot[( x + 1)/Exp[x^2], {x, -5, 5}] where one y value corresponds to multiple x values. Mar 21, 2022 at 13:44
• First, you can divide everything by a, introduce y1=y/a and study the problem with one variable b/a. Second, the important question is: "What are you going to do with your solution, provided you have obtained it?" May it be that an approximate analytical solution will be OK with you? If yes, then what are the limits of variation of b/a? Can it be that you only need to plot it for various b/a values? If yes, then what is the range of x? Mar 21, 2022 at 14:25