Place a small object on the number line below at the position marked zero. Draw a circle around the object. Mark the center of this circle with the symbol for “initial position”. Move the object 5.0cm to the right and stop. Label this circle with the correct symbol for “final position.”  (A) What was the initial position of the object?     (B) What is the final position of the object?     (C) What is the distance traveled by the object?     (D) What is the displacement of the object?     (E) Of the three underlined quantities, which are numerically equal?

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .