G(x), F(x)*g(x), (f/g)(x) Given F(x)=x^2-2x And G(x)=x+9? | Socratic

How do you find #f(x)+g(x), f(x)-g(x), f(x)*g(x), (f/g)(x)# given #f(x)=x^2-2x# and #g(x)=x+9#? Precalculus Functions Defined and Notation Function Composition

1 Answer

marfre Feb 18, 2017

#f(x) + g(x) = x^2-x +9 # #f(x) - g(x) = x^2-3x-9 # #f(x) * g(x) = x^3+7x^2-18x# #(f/g)(x) = (x(x-2))/(x+9)#

Explanation:

Substitute the functions into the equations and add like-terms:

#f(x) + g(x) = x^2-2x + x+9 = x^2-x +9#

Distribute the negative and add like-terms: #f(x) - g(x) = x^2-2x - (x+9) = x^2-2x -x-9 # #= x^2-3x-9#

Distribute and add like-terms: #f(x) * g(x) = (x^2-2x)(x+9) = x^3+9x^2-2x^2-18x# #= x^3+7x^2-18x#

Factor numerator: #(f/g)(x) = (x^2-2x)/(x+9) = (x(x-2))/(x+9)#

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