Diffusion

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question:f Dexter decides to purchase an iPhone 12 with a 15% discount and an iWatch with a 10% discount, with the original prices being 800 and 300 respectively, and a further 2% cashback discount upon checkout, what would be the total cost of the items after applying all the discounts?

answer:The discount for the iPhone 12 is 15%, so the price after the discount is 800 - (15% * 800) = 800 - 120 = 680 The discount for the iWatch is 10%, so the price after the discount is 300 - (10% * 300) = 300 - 30 = 270 The total cost of the items before the cashback discount is 680 + 270 = 950 The cashback discount is 2%, so the total cost after the cashback discount is 950 - (2% * 950) = 950 - 19 = 931 Therefore, the total cost of the items after applying all the discounts is 931 931 The answer is: 931

question:Given f(x) = frac{3}{2-x}, if g(x) = frac{1}{f^{-1}(x)} + 9, what is the value of g(3)?

answer:To find g(3), we need to find f^{-1}(3). Since f(x) = frac{3}{2-x}, we have y = frac{3}{2-x}. Solving for x, we get x = 2 - frac{3}{y}. This means f^{-1}(x) = 2 - frac{3}{x}. Substituting x = 3, we get f^{-1}(3) = 2 - frac{3}{3} = 2 - 1 = 1. Now we can find g(3): g(3) = frac{1}{f^{-1}(3)} + 9 = frac{1}{1} + 9 = 1 + 9 = boxed{10}. The answer is: 10

question:f Carla spends 10 minutes sharpening her knife and three times that amount of time peeling vegetables, what is the total amount of time she spends on these activities?

answer:Carla spends 10 minutes sharpening her knife. She spends three times that amount peeling vegetables, which is 10 x 3 = 30 minutes. The total amount of time she spends on these activities is 10 + 30 = 40 minutes. 40 The answer is: 40

question:Determine the range of the function f(x) = lfloor xrfloor - x. Express your answer in interval notation.

answer:The function f(x) = lfloor xrfloor - x is equal to the integer part of x minus x. The integer part of x is the greatest integer less than or equal to x. So, for any x in the interval [n,n+1), where n is an integer, f(x) = n - x. The range of f(x) is the set of all possible values of f(x). For each integer n, the value of n-x is always in the range (-1,0]. Therefore, the range of f(x) is boxed{(-1,0]}. The answer is: (-1,0]