I would like to generate 200 invertible functions.
Currently, I pass a function to Solve, which solves the function symbolically with respect to a specified variable.
For instance,
Solve(x/(1 + x) == y, x)
returns
expression(list(x == y/(1 - y)))
I take this expression and switch the x's and y's:
y = x/(1 - x)
However, I want to make sure that I only pass invertible functions to Solve. There are no constraints on the functions, though I'd like to include a good variety of trigonometric functions and exponents. I'm trying to provide middle and high school students with diverse practice with inverting functions.
Is there a way to manipulate $y=a(x+b)^{(2n+1)}+c$ or $y=\frac{a+bx} {c+dx}+d$ so that it involves trig functions like $cos$/$sin$/$tan$?