Suppose the functious f, g, h, r and are defined as follows: 1 loga logg F - = (ar - 3) = 5x-2x = 2x+1-2-2 = T 1.1 Write down Dr, the domain off and then solve the equation f(2)=-log V. 1.2 Write down D, and then solve the equation g(x) = - 1.3 Write down D,, and then solve the inequality 22h (a). 1.4 Write down D, and then solve the equation r(a) = 0. 15 Write down Dr without first calculating (r-) (z). 16 Write down D without first calculating (2). Question 2 V(-3,4) R(3.2) S T e The sketch shows the graph of a fimction f, which is a straight line defined by y = ma+k such that the point V lies on the line, and the graph of a function g, which is a parabola with vertex R. The straight line and parabola intersect at P and Q. The points S and T lie on the parabola and straight line, respectively, between P and Q. The line ST is parallel to the y-axis. 2.1 Calculate mand k, and hence write down the equation for f. 2.2 Find the equation of the parabola. A y=f(x) 2.5 What is the equation of the hyperbola through the point V? 2.0 Use the graphs to solve the inequality (f-g) (2) 20. (3) 2.3 Find the maximum length of ST. At what value of r will ST be at its longest? (5) 2.4 What is the equation of the circle with centre P and radins equal to the distance from P to the origin? (1) (3) [20]