Functions (AQA GCSE Further Maths)

f           for all

g

Work out the value of gf(4)

[2]

Show that fg can be written in the form  where  is an integer.

[2]

The function f is given by   

The range is 

Work out the domain of the function.

[1]

The function g is given by with domain

Work out the range of the function.

[2]

The function h is given by 

Work out

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A function f is given by

A sketch of is shown.

Work out all the values of for which   

[4]

g is a function such that    
Work out an expression for

[1]

k is a function such that
Work out an expression for    

[2]

A function is given by   

Draw the graph of on the grid.

[4]

Solve 

You must show your working.

[6]

The domain of is    ⩽ 3

Work out the range of .

[2]

g

The domain of g() is

Work out the range of g().

[2]

f() is a function with domain all values of .

 where is a constant.

Work out the possible values of .
Give your answer as an inequality.

[4]

for all real values of .

Solve 

You must show your working.

[4]

On the grid, draw the graph of     

[4]

     for all values of 

     for 

Work out the range of .

Give your answer as an inequality.

[1]

Work out the range of g.

Give your answer as an inequality.

[2]

Solve  =g

You must show your working.

Give your answers to 3 decimal places.

[4]

For each of these two function machines, when the input is  the output is .

     and            and       

Work out an expression for  in terms of .

Give your answer in its simplest form.

[6]

The function      has domain    

Here is the graph of   

Write down the range of for domain  

[2]

 for positive values of .

Work out   

Give your answer as a fraction in its simplest form.
You must show your working.

[5]