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Rational EquationGiven:f(x) = 5-x-3x² Compute: f(x+h) – f(x)
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It is given that f(x) = 5 - x - 3x^2
f(x+h) - f(x)
=> 5 - (x+h) - 3(x+h)^2 - (5 - x - 3x^2)
=> 5 - x - h - 3x^2 - 3h^2 + 6xh - 5 + x + 3x^2
=> - h - 3h^2 + 6xh
The required value of f(x+h) - f(x) = - h - 3h^2 + 6xh
Posted by justaguide on October 30, 2011 at 2:08 AM (Answer #2)
Use formula (a+b)^2=a^2+2ab+b^2 to expand (x+h)^2.
(x+h)^2 = x^2 + 2xh + h^2
Multiply by 3 => 3x^2 + 6xh + 3h^2
Open the brackets:
f(x+h)=5 - x - h - 3x^2 - 6xh - 3h^2
Subtract f(x) from f(x+h):
5 - x - h - 3x^2 - 6xh - 3h^2 - 5 + x + 3x^2
Reduce opposite terms:
-h - 6xh - 3h^2
ANSWER: f(x+h)-f(X)= -h - 6xh - 3h^2
Posted by sciencesolve on November 26, 2011 at 12:31 AM (Answer #3)
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