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Mathematics - Functions : Transformations and Inverses

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1. Given f(x)= 4x-7, g(x)= 2x - x2, and G(x)= 3/x/+2, find f(-1) + g(3)

2. Determine if the equation y2= x2 defines y as a function of x. Justify your answer

3. Sketch by hand a graph of a function f that is decreasing on [-4,2], constant on [-2,1], and increasing on [1,2]

4. The volume of a right circular cone is given by the formula V=1/3 pi r2 h. If an ice cream cone has a volume of 14 cubic inches, and the radius plus the height equals 6 inches, what is the radius (in inches)? Give the answer to two decimal places

5. Assume f(x)= 3x3 + 2x + 1 and g(x)= 3(-x +2)3 +2(-x +2) + 4. Which sequence of transformations will change the graph of f into the graph of g?

6. Determine f-1 for f(x)= x-6/ x+4. Show your work

7. Find the inverse of the give function. Show your work

f(x)= square root of x2 + 7

8. Graph the given function and its inverse
f(x)= x2 + 2 for x >or equal 0

9. Find the domain of f(x)= square root of x + 3. Express the answer in interval notation

10. Let f(x)= x3 - 4 and g(x)= square root3 of x + 4. Show that (f o g)(x)=x and (g o f)(x)=x. Show all work

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