FALL 2009, MAP 103 ALGEBRA, FINAL REVIEW(1) Expressyas a function ofxfor the expression: log3y= 2 + 4 log3(2x).(2) Supposef(x) =√x+ 1, g(x) = 2x-1,andh(2) = 3.Findf◦g◦h(2).(3) Letf(x) =12x-13.Write a formula for the inverse and check thatf◦f-1(x) =x.(4) Determine if the following are true or false. CircleTfor true orFfor false. If false, providea counter-example.(a)T|F: log(a+b) = log(a) + log(b) fora, b≥0(b)T|F: 2x·2x= 22x(c)T|F: logrx2y3z4!=12[log(2x) + log(3y)-log(4z)](d)T|F: log(ab) = log(a) log(b) fora, b≥0(5) Evaluate: log22 + log2√2 + log222+ log 212.(6) Letf(x) =x2+ 6x+ 9.(a) What are the coordinates for the vertex?(b) How many values ofxsatisfy the equationf(x) = 0?(c) What is the equation of the line that passes through the vertex that has slope 0?(d) What is the new equation forf(x) after the transformationf(x+ 1) + 1?(7) A catapult launches a rock into the air. The motion of the rock is modeled by the equationm(t) =-1000t2+18000t+26000.Suppose that down range there is a castle with a defensivewall 108,000 feet high.