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1.8: Functions and Mathematical Models

Difficulty Level: At Grade Created by: CK-12

1. (1/2)x2 +5x+5
2. (1/2)x2-3x+5
3. 2x3+ (3/2)x2-5x
4. h(x)=4x512x2+x=8x10x2+2x\begin{align*}h(x)=\frac {4x-5}{\frac {1}{2}x^2+x} = \frac {8x-10}{x^2+2x}\end{align*} . The domain is the set of all real numbers, except x ≠ 0,x ≠ -2.
5. f(g(x))=f(x+8)=(x+8)3 g(f(x))=g(x3)=x3+8 They are never equal.
6. The graph of f(g(x)) is the graph of f(x), shifted 8 units to the left.
7. 20x-59
8. g(x)=3x+1,h(x)=x4,t(x)=f(g(x))
9. The domain of f+g is \begin{align*}\mathbb R\end{align*}. The range is y ≤ 3.25. (g/f) has the domain of all real numbers except x=0. The range is all real numbers.
10. f(g(x))= (dx+a)/(bdx+c). The domain of the function is all real numbers except x = (-c)/bd.

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