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Mathematics, 11.02.2020 19:45 skylarbrown018

The idea of a linear combination is a very general idea and appears throughout mathematics. In addition to taking a linear combination of two variables, we can take linear combinations of two functions. If we take a linear combination of two functions, we will get a new function. Let's look at an example. Let f(x)=x2−3x and g(x)=2x+2 . Then one example of a linear combination of f(x) and g(x) is 2f(x)+3g(x) We can even go a little bit farther and simplify the expression. If we do, we get 2f(x)+3g(x)=2(x2−3x)+3(2x+2)=2x2−6x +6x+6=2x2+6 Thus, we can say that 2x2+6 can be written as a linear combination of f(x) and g(x) . Determine whether each of the following functions can be written as a linear combination of f(x) and g(x) . If a function can be written as a linear combination, give the coefficients of f(x) and g(x) . If not, write NA in both coefficient boxes.

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