Final answer:
The student's question is about showing the invertibility of a linear transformation and finding its inverse formula. The details for the domains and codomains, as well as the transformation, are missing, making it difficult to provide a complete answer. Generally, one would prove the transformation is bijective and find the inverse matrix if applicable.
Step-by-step explanation:
The student has asked about a linear transformation and is seeking to demonstrate its invertibility and to find a formula for its inverse. Unfortunately, the question seems to have omitted the spaces where the domains and codomains should be, as well as the specific transformation in question. However, in general, showing that a linear transformation is invertible involves proving that the transformation is bijective (i.e., one-to-one and onto). If a transformation can be represented by a matrix, the matrix must have full rank and thus a non-zero determinant. To find the formula for the inverse transformation, one would typically first ensure that the transformation is indeed invertible, then either find the inverse matrix (for transformations represented by matrices) or provide an algebraic method for finding inverses in other cases.
To use the quadratic formula to solve for time t, one would first ensure the equation is in the standard form ax2 + bx + c = 0, and then apply the formula t = (-b ± √(b2 - 4ac))/(2a) to find the values of t. Examples provided from the student's materials indicate a use of the quadratic formula, but the context is lacking in providing clarity on the specifics of the linear transformation.