SOLUTION: (f of g)(4) (g of f)(2) (f of f)(1)
f(x)=4x^2-3
g(x)=3-1/2x^2
I've been trying to solve this equation and i have spent about two hours on it. I think my problem might just b
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Question 814799: (f of g)(4) (g of f)(2) (f of f)(1)
f(x)=4x^2-3
g(x)=3-1/2x^2
I've been trying to solve this equation and i have spent about two hours on it. I think my problem might just be the fraction part.
Found 2 solutions by jsmallt9, MathTherapy:
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Is or ? If it is the first one, then use parentheses to show that the is not in the denominator: g(x)=3-(1/2)x^2. I am going to assume that the first one is correct.
(f of g)(x) means f(g(x)):
(f of g)(x) = f(g(x))
(f of g)(x) =
(f of g)(x) =
Now we simplify. To square g(x) we can use FOIL or the pattern. I prefer to use the pattern:
(f of g)(x) =
Simplifying...
(f of g)(x) =
Multiply by 4 using the Distributive Property:
(f of g)(x) =
Re-arranging the terms and adding the constant terms:
(f of g)(x) =
(f of g)(4) =
Simplifying:
(f of g)(4) =
(f of g)(4) =
(f of g)(4) = 97
(g of f(x) = g(f(x))
(g of f(x) =
(g of f(x) =
Using the pattern again:
(g of f(x) =
Simplifying...
(g of f(x) =
Distributing the 1/2:
(g of f(x) =
Subtracting:
(g of f(x) =
Simplifying...
(g of f(x) =
(g of f(x) =
(g of f(2) =
Simplifying...
(g of f(2) =
(g of f(2) =
(g of f(2) =
(g of f(2) =
(g of f(2) =
I'll leave (f of f)(1) to you.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
(f of g)(4) (g of f)(2) (f of f)(1)
f(x)=4x^2-3
g(x)=3-1/2x^2
I've been trying to solve this equation and i have spent about two hours on it. I think my problem might just be the fraction part.
, or g(4) = - 5
f(g(4)) now becomes f(- 5)
Since , then
Use the same concept to solve the rest.
You can do the check!!
Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com. Further help is available, online or in-person, for a fee, obviously.
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