3. (a) Here is a curve drawn on Cartesian axes (the x- and y-axes increase from left to

right and upwards as usual)

Say whether or not this graph might represent each of the following equations and

explain your answer.

4. (a) Write each of the following more simply (i.e. not involving logs)

(i) log a

(b) Solve the following equations for x, giving your answers to 4 significant figures:

5. (a) Say whether each of the following is true or false:

(ii) 0.68 Q

(iii) 12 Z

(iv) –12 N

(v) 15.7 {x R: 10 < x < 20} [5]

(b) Let f:RR be given by

(i) What is the range of f? (give e.g. an answer of the sort {xR:….}) [2]

(ii) Why does f as defined have no inverse function? Explain what we have to do so

that an inverse function can be defined. Assuming this modification has been made, find an expression for