Help with One to One Function

Question

The function f(x)=(x+4)^2 is not one-to-one. Choose a largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one.
The largest possible domain is ?
the inverse function is g(x)=?

Answer 1

f(x)=(x+100)³ is an example of a one-to-one function (for every x there is one and only one y=f(x)). The domain is from -∞ to ∞, as is the range.

x+100=∛y where y=f(x), so x=(∛y)-100. If x=g(y) then g(y)=(∛y)-100, and g(x)=(∛x)-100. g(x)=f^-1(x), the inverse of f.