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. If xx is the original width of the photo and the function ff determines cropped width of the photo (in inches) in terms of xx, write a formula to define f If nn represents the width (in inches) of the cropped photo, define a function gg to determine the width (in inches) of the resized photo in terms of n. What is the final cropped and resized photo width if the original photo was 13 inches wide? Represent the value in (c), that is, the final cropped and resized photo width for a photo that was originally 13 inches wide, using function notation? (Your answer will look something like g(f(32))g(f(32)) or (f(g(19))(f(g(19)).) Complete the function definition for g∘fg∘f that combines the two processes (cropping followed by resizing) into a composite function.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
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.
- If xx is the original width of the photo and the function ff determines cropped width of the photo (in inches) in terms of xx, write a formula to define f
- If nn represents the width (in inches) of the cropped photo, define a function gg to determine the width (in inches) of the resized photo in terms of n.
- What is the final cropped and resized photo width if the original photo was 13 inches wide?
- Represent the value in (c), that is, the final cropped and resized photo width for a photo that was originally 13 inches wide, using function notation? (Your answer will look something like g(f(32))g(f(32)) or (f(g(19))(f(g(19)).)
- Complete the function definition for g∘fg∘f that combines the two processes (cropping followed by resizing) into a composite function.
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