Basic Math/Algebra..

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Expert: Josh - 12/3/2003


Question
Let f(x)=2x+3 and g(x)=x(to the power of 2). Write the function h(x)=4x(to the power of 2)+12x+8 as a composition of functions using f and g.

Answer
Hi Edyth,

I think you made a typo. It's not possible to get 4x^2+12x+8 from function composition, given f(x)=2x+3, g(x)=x^2. I think it should read h(x)=4x^2+12x+9.

Look at h(x). To obtain some multiple of x^2, we must substitute f(x) into g(x). The function g(x) effectively square its argument. That is, g(f(x)) basically square f(x) itself.
g(f(x))=[f(x)]^2 in this instance.
g(f(x))=(2x+3)^2
=(2x+3)(2x+3)
=2x(2x+3)+3(2x+3)
=4x^2+12x+9
=h(x)

Hope this helps.

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Josh

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When I work through problems, I like to emphasize concepts which I believe are worth noting. I will try to answer questions in the following areas, but not at the advanced level. Algebra. Sequences & Series. Trigonometry. Functions & Graphs. Coordinate Geometry. Quadratic Polynomials. Exponential & Logarithms. Basic Calculus. Probability, Permutation and Combination. Mathematical Induction. Complex numbers. Physics problems.

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I have worked as a teaching assistant in college. My hope is that more people will share knowledge without boundary, give help without seeking recognition or monetary rewards.

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Bachelor degree in Engineering Science

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