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The inverse notation f1 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=q(C). The following problem illustrates this idea. Under certain conditions, if a rock falls from a height of 80 meters, the height H (in meters) after t seconds is approximated by the following equation. H(t)=80-4.9t2 (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. OA. The coefficient of t2 is negative, so the function is always decreasing. A decreasing function is always one-to-one. B. The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-one. C. t represents time, so it must be greater than or equal to 0. For t≥0, H(t) is one-to-one. D. The t2 term is not the first term, so H(t) does not behave like a quadratic function. (b) Find the inverse of H and verify your result. t(H) = (Type an exact answer.)

The inverse notation f1 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=q(C). The following problem illustrates this idea. Under certain conditions, if a rock falls from a height of 80 meters, the height H (in meters) after t seconds is approximated by the following equation. H(t)=80-4.9t2 (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. OA. The coefficient of t2 is negative, so the function is always decreasing. A decreasing function is always one-to-one. B. The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-one. C. t represents time, so it must be greater than or equal to 0. For t≥0, H(t) is one-to-one. D. The t2 term is not the first term, so H(t) does not behave like a quadratic function. (b) Find the inverse of H and verify your result. t(H) = (Type an exact answer.)

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.6: Solving Quadratic Equations By Using The Quadratic Formula
Problem 28PPS
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The inverse notation f1 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=q(C). The following problem illustrates this idea. Under certain conditions, if a rock falls from a height of 80 meters, the height H (in meters) after t seconds is approximated by the following equation. H(t) = 80 - 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. The coefficient of t2 is negative, so the function is always decreasing. A decreasing function is always one-to-one. B. The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-one. C. t represents time, so it must be greater than or equal to 0. For t≥0, H(t) is one-to-one. D. The t² term is not the first term, so H(t) does not behave like a quadratic function. (b) Find the inverse of H and verify your result. t(H) = (Type an exact answer.)
Transcribed Image Text:The inverse notation f1 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=q(C). The following problem illustrates this idea. Under certain conditions, if a rock falls from a height of 80 meters, the height H (in meters) after t seconds is approximated by the following equation. H(t) = 80 - 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. The coefficient of t2 is negative, so the function is always decreasing. A decreasing function is always one-to-one. B. The parabola opens to the right, so it passes the horizontal line test. Thus, H(t) is one-to-one. C. t represents time, so it must be greater than or equal to 0. For t≥0, H(t) is one-to-one. D. The t² term is not the first term, so H(t) does not behave like a quadratic function. (b) Find the inverse of H and verify your result. t(H) = (Type an exact answer.)
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