# Change in y with change in x

Suppose we change x in y = f(x) from x to x+dx, then y changes from f(x) to f(x+dx). But suppose if we change y from y to y+dy, then can we determine how x changes? Why or why not? Is it because y is a function of x and not vice-versa?

lurflurf
Homework Helper
sure if f is invertible we will have x change to $$\mathrm{f}^{-1}(\mathrm{f}(x)+\mathrm{dy})$$

Take the sinus function: You cannot always determine what dx was from dy. However, if the ds are small quantities and f is differentiable, in many cases you can take the approximation ##y(x+dx)\approx l(x+dx)=f(x)+f'(x)\cdot dx##. You also know you started with ##y=f(x)##, so in linear approximation ##dy=f'(x) \cdot dx## and ##dx=\frac{1}{f'(x)}\cdot dy##. Of course, this does not always work, for example it does not work if ##f'(x)=0##.

Svein