# functions are inverses

Name Class Date 10-2 CLASSWORK Attributes of Cube Root Functions If two functions are inverses of each other, they will undo each other. You can prove that functions are inverses using the compositions f(g(x)) and g(x)). Problem Use composition of functions to determine whether f(x) = Vx+2 are inverses. Explain. and g(x)=x3-2 Find the compositions/(g(x)) and g(x)). $(8(x)) = 323-2+2 = X $((x)) = (x+2)3 – 2 = 3×3 = X Since f(g(x)) = x and g(/(x) = x, f(x) and g(x) are inverses. Use composition to prove that f(x) and g(x) are inverses. Check your work. $(x) = Vx+13; g(x) = (x -13) 1. 2. f(x) = x3 + 1; g(x) = 2x-1 | 10-2 CLASSWORK (continued) Attributes of Cube Root Functions Because the domain and range of cube root functions are all real numbers, there is no absolute maximum or minimum for the function. The same is true for cubic functions, the inverse of cu be root functions. However, you can find a local maximum and minimum. Problem Graph the cube root function. What are the minimum and the maximum on the given interval? f(x) = {x + 4; [1, 8] +y 8 6 4 2 8 6 4 -2 O 2 4 6 00 -2 -4 -6 -8 For the given interval, the graph rises as x increases, so the minimum and maximum values of the function occur at the endpoints of the interval. The minimum value on the interval is f(1) = 5 and the maximum value on the interval is (8)=6. Use the graph in the Problem above to analyze the maximum and minimum values for the given interval. 3. (-8, 0] 4. (-1, 1]

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