The inverse notation f-1 used in a pure mathematics problem

Last updated: 7/21/2022

The inverse notation f-1 used in a pure mathematics problem is not always used when finding inverses of applied problems. Rather, the inverse of a function such as C=C(q) will be q=qC). The following problem illustrates this idea. Under certain conditions, e a rock falls from a height of 50 meters, the height H (in meters) after t seconds is approximated by the following equation H(t)=50-4.9t² (a) in general, quadratic functions are not one-to-one. However, the function H(t) is one-to-one. Why? Choose the correct answer below A. t represents time, so it must be greater than or equal to 0. For t≥0, H(t) is one-to-one B The t2 term is not the first term, so H(t) does not behave like a quadratic function C The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-one D The coefficient of t2 is negative, so the function is always decreasing. A decreasing function is always one-to-one (b) Find the inverse of H and verify your result (Type an exact answer) (c) How long will it take a rock to fall 30 moters? It will take a rock approximately seconds to fall 30 meters (Round to the nearest hundredth as needed)