A = 6 x^2 + 6x is equal to x(x+6) b=2 Denominator and numerator of the first term are multiplied by x. c=6 Second term is multiplied by (x-6)/(x-6) d=2 Now that they have the same denominator, the two terms are combined. 2 is the coefficient of the first term e=6 In the same way as d is carried over from b, e is carried over from c. f = 6 2x - x + 6 = x + 6 g = 1 We factor out the (x+6) from the numerator and denominator
We have to determine which value is equivalent to | f ( i ) | if the function is: f ( x ) = 1 - x. We know that for the complex number: z = a + b i , the absolute value is: | z | = sqrt( a^2 + b^2 ). In this case: | f ( i )| = | 1 - i |. So: a = 1, b = - 1. | f ( i ) | = sqrt ( 1^2 + ( - 1 )^2) = sqrt ( 1 + 1 ) = sqrt ( 2 ). Answer: <span>C. sqrt( 2 )</span>