23.03.2023 - 10:36

Suppose you want to crop (remove) 4 inches from the width of a photo. After you have cropped (reduced) the width of the photo by 4 inches, you resize the photo by making it 40% of its cropped size. (a) If x is the original width of the photo and the func

Suppose you want to crop (remove) 4 inches from the width of a photo. After you have cropped (reduced) the width of the photo by 4 inches, you resize the photo by making it 40% of its cropped size.

(a) If x is the original width of the photo and the function f determines cropped width of the photo (in inches) in terms of x, write a formula to define f.

(b) If n represents the width (in inches) of the cropped photo, define a function g to determine the width (in inches) of the resized photo in terms of n.

(c) What is the final cropped and resized photo width if the original photo was 19 inches wide?

Answers (1)
  • anf
    March 31, 2023 в 23:27

    (a) Let c be the width (in inches) that needs to be cropped from the original photo of width x. Then, the cropped width of the photo is given by:

    f(x) = x - c

    Substituting c = 4, we get:

    f(x) = x - 4

    (b) Let w be the width (in inches) of the resized photo, and n be the width (in inches) of the cropped photo. Then, the width of the resized photo is given by:

    g(n) = 0.4n

    Substituting n = f(x) = x - 4, we get:

    g(f(x)) = 0.4(x - 4)

    (c) If the original photo was 19 inches wide, then its cropped width is:

    f(19) = 19 - 4 = 15 inches

    The width of the resized photo is:

    g(f(19)) = 0.4(19 - 4) = 6.2 inches (rounded to one decimal place)

    Therefore, the final cropped and resized photo width is 6.2 inches when the original photo is 19 inches wide, after cropping 4 inches and then resizing to 40% of the cropped width.

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