Rational expressions

Given that k is a negative constant and that the function f(x) is defined by

Hence find f ' (x), giving your answer in its simplest form.

State, with a reason, whether f(x) is an increasing or a decreasing function. Justify your answer.

Express

as a single fraction in its simplest form.

Find the range of g.

Find the exact value of a for which g(a) = g^–1(a).

Express

as a single fraction in its simplest form. (4)

Express

as a single fraction in its simplest form.

Show that

The curve C has equation y = f (x). The point P −1, − lies on C.

Find an equation of the normal to C at P.

Simplify fully

Given that ln(2x² + 9x− 5) = 1+ ln(x² + 2x 15), x 5,

find x in terms of e.

Express

as a single fraction in its simplest form.

The function f is defined by

The function g is defined by

Find the exact values of x for which g ( x) = 1

Express f (x) as a single fraction in its simplest form.