SOLUTION: PLEASEEE 1. Find functions f and g so that f [g(x)] = H(x) where H(x)=(1+x^2)^3 2. If g(x)=x^2+4x+2 find g(2) and g(x+2) 3. For f(x)=4x+1 and g(x)=x^2-2x-4 find (g-f)(x).

Algebra ->  Functions -> SOLUTION: PLEASEEE 1. Find functions f and g so that f [g(x)] = H(x) where H(x)=(1+x^2)^3 2. If g(x)=x^2+4x+2 find g(2) and g(x+2) 3. For f(x)=4x+1 and g(x)=x^2-2x-4 find (g-f)(x).       Log On


   

Question 145020: PLEASEEE
1. Find functions f and g so that f [g(x)] = H(x) where H(x)=(1+x^2)^3
2. If g(x)=x^2+4x+2 find g(2) and g(x+2)
3. For f(x)=4x+1 and g(x)=x^2-2x-4 find (g-f)(x). Simplify the answer.
4.What is the function which would intersect the y-axis 2 positions up(vertical) from the function f(x)=x^2
5. Using the graphing utility to approximate any relative minimum or maximum points of f(x)=x^2-6x.
THANK YOU VERY MUCH
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
1. Find functions f and g so that f [g(x)] = H(x) where H(x)=(1+x^2)^3
g(x) = 1+x^2
f(x) = x^3
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2. If g(x)=x^2+4x+2 find g(2) and g(x+2)
g(2) = 1+2^2 = 5
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g(x+2) = 1 + (x+2)^2 = x^2 + 4x +5
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3. For f(x)=4x+1 and g(x)=x^2-2x-4 find (g-f)(x). Simplify the answer.
(g-f)(x) = x^2-2x-4 -(4x+1) = x^2 -6x -5
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4.What is the function which would intersect the y-axis 2 positions up(vertical) from the function f(x)=x^2
f(x) = x^2 +2
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5. Using the graphing utility to approximate any relative minimum or maximum points of f(x)=x^2-6x.
(3,-9)