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functions
Domain
Composition
Combination
Applications
100
Evaluate the function f(x)= x^2 + 5x + 9 at the given value. f(-9)
f(-9) = 45
100
Find the domain of the function f(x) = x^2 + 5x -3
(- ∞, ∞)
100
For f(x) = 2x -3 and g(x) = 2x^2 -4, find the following functions: f(g(x))
f(g(x))= 4x^2 - 11
100
Given f(x) = 2x^2 + 17x + 21 and g(x) = x + 7 Find (f + g) (x)
(f +g)(x)= 2x^2 + 18x + 28
100
Graph the given functions, f and g, in the same rectangular coordinate system. Describe how the graph of g is related to the graph of f. f(x) = √x and g(x) = √(x-8)
The graph g is the graph f shifted right 8 units.
200
Evaluate the function f(x)= x^2 + 5x + 9 at the given value. f(-x)
f(-x)= x^2 -5x + 9
200
Find the domain of the function f(x) = 12/(x+5)
-∞, -5) U(-5, ∞)
200
For f(x) = 2x -4 and g(x) = x^2 -5, find the following functions. (f o g)(-1)
(f o g)( -1) = -12
200
Given f(x) = 2x^2 + 17x + 21 and g(x) = x + 7 Find (f-g)(x)
(f-g)(x)= 2x^2 + 16x + 14
200
A company that manufactures bicycles has a fixed cost of $3,000 to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable cost. Write the total cost C, as a function of the number of bicycles produced, x. Find the Cost Function C(x)
C(x)= 3,000 + 300x
300
The function f(x)= 2x + 1 is one-to-one. Find an equation for the inverse function.
x-1 /2
300
Find the domain of the function f(x)= 12/ x + 11
(-∞, -11) U (-11, ∞)
300
For f(x) = 2x -3 and g(x) = 2x^2 -4, find the following functions: (f o g)(-2)
(f o g)(-2) = 5
300
Given f(x) = 2x^2 + 17x + 21 and g(x) = x + 7 Find (fg)(x)
(fg)(x) = 2x^3 + 31x^2 + 140x + 147
300
A company that manufactures bicycles has a fixed cost of $3,000 to produce each bicycle. The total cost for the company is the sum of its fixed cost and variable cost. Write the total cost C, as a function of the number of bicycles produced, x. Then find C(100)
C(100)= 33,000
400
Evaluate the function f(x)= x^2 + 5x + 9 at the given value. f(x + 7)
f(x + 7) = x^2 + 19x + 93
400
Find the domain of the function f(x) = √(x-3)
[3, ∞)
400
For f(x) = 3x -3 and g(x) = 4x^2 -5, find the following functions: (g o f)(x)
(g o f) (x) = 36x^2 - 72x + 31
400
Given f(x) = 2x^2 + 17x + 21 and g(x) = x + 7 Find (f/g) (x) (simplify your answer)
(f/g)(x) = 2x + 3
400
Use a graphing calculator to find maximum and minimum values for the function: f(x) = 2x^3 + 6x^2 -18x + 5
Max = (-3, 59) Min = (1, -5)
500
Evaluate the function f(x)= x^2 -6x -2 at the given value. f(x + 9)
f(x + 9) = x^2 + 12x + 25
500
Find the domain of the function f(x) = √(x+14)
[-14, ∞)
500
For f(x) = 2x -3 and g(x) = 2x^2 -4, find the following functions: (g o f)(x)
(g o f )(x) = 8x^2 -24x + 14
500
Given f(x) = 4x^2 -11x -45 and g(x) = x-5 find (f/g)(x) ( simplify your answer)
(f/g)(x)= 4x + 9
500
A company that sells radios has yearly fixed cost of $500,000. It cost the company $40 to produce each radio. Each radio will sell for $60. The company's cost and revenue are modeled by the following functions, where x represents the number of radios produced and sold. C(x)= 500,000 + 40x R(x)= 60x Find (R-C) (12,500)
(R-C)(12,500)= -250,000