document.write( "Question 1201268: given f(x)=x^3-2x+1 and g(x)=-x^2-5x+12 find (f+g)(x) \n" ); document.write( "

Algebra.Com's Answer #835555 by Theo(13342) $\"\"$ $\"About$

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(f+g)(x) is equal to f(x) + g(x)
\n" ); document.write( "f(x) = x^3 - 2x + 1
\n" ); document.write( "g(x) = -x^2 - 5x + 12
\n" ); document.write( "f(x) + g(x) = x^3 - x^2 - 7x + 13
\n" ); document.write( "when x = 3, you get:
\n" ); document.write( "f(x) = 3^3 - 2*3 + 1 = 27 - 6 + 1 = 22
\n" ); document.write( "g(x) = -3^2 - 5*3 + 12 = -9 - 15 + 12 = -12
\n" ); document.write( "f(x) + g(x) = 22 - 12 = 10
\n" ); document.write( "(f+g)(x) = f(x) + g(x) = x^3 - x^2 - 7x + 13
\n" ); document.write( "when x = 3, this becomes (f+g)(x) = 3^3 - 3^2 - 7*3 + 13 = 27 - 9 - 21 + 13 = 27 + 13 - 9 - 21 = 40 - 30 = 10
\n" ); document.write( "since 22 - 12 = 10, that checks out ok.
\n" ); document.write( "the rule is:
\n" ); document.write( "(f+g)(x) is equal to f(x) + g(x)
\n" ); document.write( "when you add f(x) to g(x), you combine like terms and keep the unlike terms separate.
\n" ); document.write( "the unlike terms were the x^3 term the x^2 term.
\n" ); document.write( "the like terms were the x terms and the constant terms.
\n" ); document.write( "x^3 and x^2 were kept separate.
\n" ); document.write( "-5x and -2x were added together.
\n" ); document.write( "+1 and +12 were also added together.
\n" ); document.write( "the result was x^3 - x^2 - 7x + 13
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