College Algebra & Trigonometry, 2018a

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4.8. INVERSE FUNCTIONS 229 4.8 Inverse Functions An inverse function undoes the action of the original function. So the inverse of a function that squared a number would be a function that square rooted a number. In general, an inverse function will take a y value from the original function and return the x value that produced it. We can see this in an application. Given an object with little or no air resistance that is dropped from 100 ft., the function that describes its height as a function of time would be: H(t) = 100 − 16t 2 In this function, H(t) is the height of the object at time t. If we wanted to turn this around so that it described the time for a given height, then we would want to isolate the t variable. In this example, the graph of the function would change in that the original independent variable - t, becomes the dependent variable in the inverse function. h = 100 − 16t 2 16t 2 = 100 − h t 2 = 100 − h 16 t = √ 100 − h 16 T (h) = √ 100 − h 4
230 CHAPTER 4. FUNCTIONS Original function: H(t) =100− 16t 2 100 H(t) t 75 50 25 1 2 3 4 Inverse function: T (h) = 4 √ 100 − h T (h) 4 3 2 1 25 50 75 100 h Notice that the graph of the function inverse is the original function reflected over the line y = x, because an inverse function interchanges the independent and dependent variables.
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College Algebra & Trigonometry
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c○2018 Richard W. Beveridge This
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288 CHAPTER 6. SEQUENCES AND SERIES
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College Algebra & Trigonometry, 2018a

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