Summer Review Packet for Students Entering Pre-Calculus Example: Rewrite f(x) as y Summer Review Packet for Students Entering Pre-Calculus f (x ) = Vx+1 Multiplying and Dividing: Factor numerator and denominator completely. Cancel any common factors in the top y = Vx+1 Switch xand y and bottom. If dividing, change divide to multiply and flip the second fraction. x= Vy+1 Solve for your new y By. *2 + 10x + 21 x2 +2x-15 5-4x-x2 x3+4x2 -21x Factor everything completely. ( x )' = ( VJ+ 1 ) Cube both sides x' = y+1 Simplify (x + 7) (x + 3 ) ( x + 5) (x - 3 ) Cancel out common factors in the top and bottom. (5+ x)(1- x) x(x-3)(x+7) y=x'-1 Solve for y f-1 ( x ) = x3 -1 Rewrite in inverse notation ( x + 3) Simplify. x (1 - x ) Find the inverse , f-' (x ) , if possible. 74. f (x ) = 5x+2 75 . f ( x ) = 1x - 1 76. 523 + 2 2 - z 77 m' - 25 78. 3s 3z m 2 + 5m 2152 573 E8 a - 5a+6 3a +12 a+ 4 80 . 6d-9 6-13d +6d2 a - 2 5d+1 15d2 -7d-2 Rational Algebraic Expressions: Addition and Subtraction