![]() ![]() (a) Open the Java Calculator and enter the formulas for f and g. Then g is the inverse of f and f is the inverse of g. Letting f -1 denote the inverse of f, we have just shown that g = f -1. We also need to see that this process works in reverse, or that f also undoes what g does.į(g(x)) = f((x - 1)/2) = 2(x - 1)/2 + 1 = x - 1 + 1 = x. This simplification shows that if we choose any number and let f act it, then applying g to the result recovers The way to check this condition is to see that the formula for g(f(x)) = x must hold for all x in the domain of f. In other words, g must take f(x) back to x for all values of x in the domain of f. ![]() To prove that g is the inverse of f we must show that this is true for any value of x in Then g(7) = 3, g(-3) = -2, and g(11) = 5, so g seems to be undoing what f did, at leastįor these three values. In other words, the inverse of f needs to take 7 back to Now that we think of f as "acting on" numbers and transforming them, we can define the inverse ofį as the function that "undoes" what f did. Helps to think of f as transforming a 3 into a 7, and f transforms a 5 into an 11, etc. We know how to evaluate f at 3, f(3) = 2*3 + 1 = 7. P.158 #1-4, 5, 8, 9, 12, 13, 15, 18, 21, 22, 27, 31, 34, 37, 46, 48, 51, 71, 74, 83 Definition of Inverse Function Graphs of Inverse Functions Existence of an Inverse Finding Inversesīefore defining the inverse of a function we need to have the right mental image of function.Ĭonsider the function f(x) = 2x + 1. Contents: This page corresponds to § 1.7 (p.
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