Functions (Edexcel IGCSE Maths A: Higher)

Express  in the form 

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 

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

The function f is defined as

Find f (8)

Express the inverse function in the form  = ......

The function is defined as

Which values of cannot be included in a domain of ?

Express the function  in the form = .......

Give your answer as simply as possible.

State one value of which cannot be included in any domain of f.

Find the value of f(0)

Find the value of for which

Show clear algebraic working.

 The diagram shows parts of the graphs of and . 

 Find g(0) 

 Find f(–1) 

State which value of cannot be included in the domain of f or .

Solve 

Express the inverse function  in the form 

f: → 21  :→  where ≠ 1

Express the composite function gf in the form f: → .....

Give your answer as simply as possible.

Express the inverse function in the form → ......

The functions and h are defined as

Find the value of (1)

State which value of must be excluded from any domain of 

Find

Simplify your answer

Express the inverse function  in the form  = .....

Find the value of 

State which value of must be excluded from any domain of f

Find 

State the value which cannot be in any range of f

f is the function such that

Find f(0.5)

Find ff(−1)

Find the value of  that cannot be included in any domain of f

Express the inverse function  in the form = ......

Show clear algebraic working.

The function f is such that  where Express the inverse function in the form

Two functions,  and  are defined as

Given that 
express the inverse function  in the form 

..................... 

and 

Show that  

 for all values of .

for all values of .

Work out .

Give your answer in the form    where  and are integers.

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.

Work out the values of and .

.........................

.........................

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 .

Find f(10)

State which values of  must be excluded from a domain of f

Find f

One of the solutions of , where  is a number, is 

Find the other solutions
Give your answers correct to 1 decimal place

For which values of  does the equation  have only one solution?

Find an estimate for the gradient of the curve at the point where  = −2.5

State which value of  must be excluded from any domain of 

The function is defined as

       with domain

Express the inverse function g⁻¹ in the form

................................................... 

State the domain of 

The functions and are such that

The function is such that

The domain of is

Express the inverse function in the form

The functions and are defined as

Find

Express the inverse function in the form 

...............................

The functions and are such that

The function  is such that 

Express the inverse function  in the form  = .........

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

The function is such that       for

Express  in the form  where  and  are constants.

Using your answer to part (a), find the range of values of  for which  is positive.

 is the function with domain such that 

Write down the range of 

Express the inverse function  in the form 

The function f is defined as for  and where  is a positive number.

Find the value of  for which 

The function  is defined as

Given that  find an expression for  in terms of .

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 

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.

and are constants.

Work out the value of .