Let f(x) = -2x + 7 and g(x) = -6x + 3. find f. g and state its domain.

Both functions are polynomials, so they are defined everywhere.

When you compute the composite function , you want to give the output of as input to .

So, the workflow is the following:

1. Choose a number x.

2. Compute g(x). This is a new number, say z.

3. Compute f(z).

As we already stated, since f is a polynomial, it accepts every real number as input, so we must not worry about what the output of g will be. This means that the domain of the composite function is still .

As for the composite function itself, we have

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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