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Find (f composed with g)(x) and (g composed with f)(x)?
f(x)=2x^3 - 3x^2 +4x - 1
g(x)= 2
I got (f composed of g)(x)=11 is this correct?
What is (g composed with f)(x)? Will it be no solution,2, or all real numbers? Please explain your answer.
6 Answers
- ?Lv 71 decade agoFavorite Answer
The language of the question is the hardest part. By substituting x = 2 we find f(x) = 11 and your answer is correct.
(g composed with f)(x) is the last line of the question, namely =2 .
- Anonymous1 decade ago
The function (f composed with g)(x) is read "f of g of x," so for g(x) = 2 it would be:
f(g(x)) = 2(g(x)^3) - 3(g(x)^2) + 4g(x) - 1
= f(2)
= 2(2^3) - 3(2^2) + 4(2) - 1
= 11
Since g(x) = 2 for all x, and f(x) gets plugged into g(x) when you find (g composed with f)(x), g(f(x)) will always be 2 no matter what f(x) turns out to be. The answer is "all real numbers" because setting x equal to any real number will give you the same result.
- Deomachus .Lv 41 decade ago
You're right about 11, and g composed with f I'm pretty sure would be 2, since there are no variables in g(x).
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- 1 decade ago
(f composite g)=(f o g)(x), to get the value of it, you will substitute the value of g(x) to all x in f(x),
therefore,
(f o g)(x)=
2(2)^3-3(2)^2+4(2)-1
2(8)-3(4)+8-1
16-12+8-1
(f o g) = 15
since there is no x in g(x), there is no solution for (g o f)(x).
- Anonymous5 years ago
f(x) is the outside function, so start with 4x - 2 g(x) gets inserted into f(x) as 4(x^2) - 2 h(x) gets inserted into f(g(x)) as 4(6 - x)^2 - 2 Now solve: 4(6 - x)^2 - 2 4(x^2 - 12x + 36) - 2 4x^2 - 48x + 144 - 2 4x^2 - 48x + 142 If you wanted to simplify it further you could finish with: 2(2x^2 - 24x + 71)