Functions (AQA GCSE Maths)

Express  in the form 

The function is such that

Find

The function  is such that

where  is a constant.

Given that 

work out the value of

The functions  and  are such that

Find

Given that ,

show that

and 

Show that  

 for all values of .

for all values of .

Work out .

Give your answer in the form    where  and are integers.

Work out the values of and .

.........................     

.........................     

for all values of

Jenny says,

“f(10) must equal 2 × f(5), because 10 is 2 × 5”

Is Jenny correct?
Show working to support your answer.

Solve   

Work out 

Give your answer in the form        where  and  are integers.

Work out 

Solve  

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

A function machine is shown below.

If the Input is 3, the Output is 5.
If the Input is 7, the Output is 25.

Use this information to fill in the two boxes.

Show that  can be written as  

State the value of .

Find the inverse function   in the form 
Show your working clearly.

The functions  and  are such that

where  and  are constants.

Find the value of  and the value of .

The functions and are such that        and           

Find 

Give your answer as a single algebraic fraction expressed as simply as possible.

Express the inverse function  in the form 

Solve 

Work out the value of  

  and     

Simplify 

  for all values of

On the grid, draw the graph of the inverse function   for  

For all values of

On the grid, draw the graph of the composite function    for 

and are constants.

Work out the value of .

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.