Functions

Here is function A.

The diagram shows a composite function with an input, n, and an output of 96.

Find the value of n.

n = .....................................................

Here is a function.

The output of function A is x.

Write an algebraic expression, in terms of x, for the input of function A.

A number, , is put into function A.
The output is also .

Find the value of .

= .....................

A function is represented by the following function machine.

A number is input into the machine.
The output is used as a new input.
The second output is 11.

Work out the number that was the first input.

A number is input into the machine.
The output given is the same number.

Work out the number.

Here is function A.

A number, k, is input into function A.
The output is also k.

Find the value of k.

k = .....................................................

Here are two functions.

Find an algebraic expression for the output of the inverse of function A when the input is x.

Here is a composite function C.

Find the value x when z = 4x .

x = ..................................................

Here are two function machines, A and B.

Both machines have the same input.

Work out the range of input values for which

                                   the output of A is less than the output of B. 

Function 1 is given by

Function 2 is given by

The inverse of the composite function 'Function 1 followed by Function 2' is given by

Find the value of .

Function 1 is given by

where . Function 2 is given by

Two different composite functions are formed: 'Function 1 followed by Function 2' and 'Function 2 followed by Function 1'.

Find the input, , for which the outputs of the two different composite functions are the same, giving your answer in terms of .