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The inverse notation f-1 used in a pure mathematics problem is not always used when...

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Calculus

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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 equationH(t)=50-4.9t(a) in general, quadratic functions are not one-to-one. However, the function H(t) is one-to-one. Why?Choose the correct answer belowA. t represents time, so it must be greater than or equal to 0. For t?0, H(t) is one-to-oneB The t2 term is not the first term, so H(t) does not behave like a quadratic functionC The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-oneD 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)

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