Let y = f(x) = e**x +x**2. Show that there exists a neighborhood I ⊂ R of the point x0 = 0 such that f : I → U := f(I)

Post by **answerhappygod** » Wed May 04, 2022 10:51 am

Let y = f(x) = e**x +x**2.
Show that there exists a neighborhood I ⊂ R of the point x0 = 0
such that f : I → U := f(I) is invertible.
Let x = φ(y) be the corresponding inverse mapping. Calculate the
2nd order Taylor expansion for φ at the point y0 = f(x0).
Note: Differentiate the equation φ(f (x)) = x.

Answer Happy

Let y = f(x) = ex +x2. Show that there exists a neighborhood I ⊂ R of the point x0 = 0 such that f : I → U := f(I)

Let y = f(x) = ex +x2. Show that there exists a neighborhood I ⊂ R of the point x0 = 0 such that f : I → U := f(I)