The principal square root function - the inverse of the square of x (or quadratic) function Definition of the inverse function The graph of the principal square root function Translation of the principal square root function in the direction of the x-axis
The principal square root function - the inverse of the square of x (or quadratic) function
Definition of the inverse function
The inverse function is a function, usually written f -1, whose domain and range are respectively the range and domain of a given function f, that is
 f -1(x) = y  if and only if   f (y) = x,
 or it is the function whose composition with the given function is the identity function, i.e.,    In order that the inverse should have a unique value for each argument, and so be properly a function, the extraction of positive square roots is the inverse of squaring, since however, without the restriction to positive values, the square root function on the domain of real numbers does not have an inverse.
The graph of the principal square root function
The graph of the inverse function is the reflection about the line y = x of the graph of a given function.
A function f has an inverse if and only if when its graph is reflected about the line y = x, the result is the graph of a function that passes the vertical line test.
A relation is a function if there are no vertical lines that intersect the graph at more than one point. Translation of the principal square root function in the direction of the x-axis
Horizontal line test
A function f has an inverse if no horizontal line intersects the graph of f more than once.
If any horizontal line intersects the graph of f more than once, then f does not have an inverse.
A mapping associating a unique member of the codomain with every member of the domain of a function is called one to one correspondence.
A function f is one-to-one if and only if f has an inverse.
Given   f (x) = x2 + y0    and, since     f [f -1(x)] = x
therefore,     f [f -1(x)] = [f -1(x)]2 + x0 = x,        or       [f -1(x)] = x - x0
 then To find the y-intercept, set x = 0 and solve for y, that is, The graph of translated principal square root function in the direction of the x-axis    College algebra contents 