INVERSESTo find the inverse of a function, simply switch the x and the y and solve for the new "y" value.Recall f¹(x) is defined as the inverse of f(x)Example 1:f(x)=√√x+1y = √√x+1= √√/y+1(x)³ =(√y+1)x³ =y+ly=x³ -1f'(x)=x³-1X =23. f(x)=2x+15x-2Rewrite f(x) as ySwitch x and yFind the inverse for each function.25. g(x)=-Solve for your new yCube both sidesSimplifySolve for yRewrite in inverse notation28. Explain how the graphs of ƒ(x) and ƒ˜¹(x) compare.ƒ-¹(x)824. f(x) =f(x)27. If the graph of f(x) has the point (2, 7) then what is one point that will be on the graph of f¹(x)?26. y=√√4-x+1

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Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter7: Polynomial Equations And Factoring

Section: Chapter Questions

Problem 2CA

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The domain of function f is (1,) and the range of function f is (,2)Find the domain and range of the inverse function.
inverse of the function x= 2/ y-3
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1. Solve for (f-1)'(3) if f(x) = x3 + x +1 2. For the function f(x)=x-1/2, x>0. Find: a. the inverse function (assume that f(x) is a one-to-one function) b. find the derivative of the inverse.
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Strontium 90 (Sr-90), a radioactive isotope of strontium, is present in the fallout resulting from nuclear explosions. It is especially hazardous to animal life, including humans, because, upon ingestion of contaminated food, it is absorbed into the bone structure. Its half-life is 27 years. Find the function Q(t)that expresses the amount of Sr-90 present at time t, where Q0is the amount present initially and t is measured in years. Q(t) = If the amount of Sr-90 in a certain area is found to be 16 times the "safe" level, find how much time (in years) must elapse before the safe level is reached. Olivia plans to secure a 5-year balloon mortgage of $250,000 toward the purchase of a condominium. Her monthly payment for the 5 years is calculated on the basis of a 30-year conventional mortgage at the rate of 5%/year compounded monthly. At the end of the 5 years, Olivia is required to pay the balance owed (the "balloon" payment). What will be her monthly payment for…
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To find the inverse of a function, simply switch the x and the y and solve for the new "y" value. Recall f'(x) is defined as the inverse of f(x)