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7.7 Operations on Functions

7.7 Operations on Functions. What you’ll learn: To find the sum, difference, product and quotient of functions. To find the composition of functions. Operations with functions. Sum (f+g)(x) = f(x)+g(x) Difference (f-g)(x) = f(x)-g(x) Product (f·g)(x) = f(x)·g(x)

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7.7 Operations on Functions

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  1. 7.7 Operations on Functions What you’ll learn: To find the sum, difference, product and quotient of functions. To find the composition of functions

  2. Operations with functions Sum (f+g)(x) = f(x)+g(x) Difference (f-g)(x) = f(x)-g(x) Product (f·g)(x) = f(x)·g(x) Quotient (f/g)(x) = f(x)/g(x) g(x)≠0

  3. Given f(x)=3x²+7x and g(x)=2x²-x-1, find each function: • (f+g)(x) • (f-g)(x) • (f·g)(x)

  4. Composition of functions If f and g are functions such that the range of g is a subset of the domain of f. Then the composite function f g can be described by the equation [f g](x) = f[g(x)]. [f g](x) is defined only if the range of g(x) is a subset of the domain of f(x). Also, [g f](x) is defined only if the range of f(x) is a subset of the domain of g(x). If given equations, plug one equation in place the variables in the other equation and simplify.

  5. If f(x)={(2,6),(9,4),(7,7),(0,-1) and g(x)={(7,0),(-1,7),(4,9),(8,2)} Find f g and g f f g = {(7,-1),(-1,7),(4,4),(8,6)} g f = {(9,9),(7,0),(0,7)}

  6. Find [f₀g](x) and [g₀f](x) for f(x)=3x²-x+4 and g(x)=2x-1 [f₀g](x) [g₀f](x)

  7. Homeworkp. 38718-46 even

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