Inequalities

The diagram shows the line y = 5 – x

On the diagram above, sketch the graph of y = │x² – 4x│, including all parts of the graph where it intersects the line y = 5 – x

(You do not need to show the coordinates of the points of intersection.)

Find the solution of the inequality

│x² – 4x│> 5 – x

Give your answer in an exact form.

The function f is defined by

Find the set of values of x for which

Give your answer in set notation.

The function f is defined by

Fully factorise f (x)

Hence, solve the inequality f (x) 0

The new graph is then reflected in the x-axis, to give the graph of y g(x)

Find the other three roots.

Find the value of a and the value of b

Solve the inequality

Fully justify your answer.

Let

where n 1

Use the method of differences to show that

where a, b and c are integers.