math hmwk... restrict the domain of f so that f^-1(x) is also a function?

Question

do u restict the original f(x) or its inverse? and how do u know the restictions?

Answer 1

You restrict the domain of the function as necessary in order that it pass both the vertical and horizontal line test. Once you do that, f^-1 exists. For example, if f(x) = sinx, you can restrict its domain to (-pi/2, pi/2). This function will then pass both h & v line test, and its inverse will then exist.

another example - f(x) = x^2. A parabola opening upward whose vertex is the origin, and fails the h-line test. If you restrict domain to (>=0), f^-1 will then exist.

Answer 2

this restriction of domain would mean that f(x) should be a one to one function. If f-1(x) is also a function, it should pass the vertical and horizontal line test