Functions

Express the inverse function in the form 

Find 
Simplify your answer.

f is a function such that

Find

 is a function such that

Find

Give your answer as simply as possible.

is the function 

Find

Express the inverse function  in the form =

is the function 

Find

The functions  and  are defined as

Work out

Work out  

Work out the value of .

Express the inverse function  in the form  = ...

f is the function such that  f(x) = 2x - 5
g is the function such that g(x) = x² - 10

Find f (4)

Find fg(-4)

Express the inverse function f^-1 in the form f^-1 (x) = ...

Solve gf (x) = -1

The functions and are such that

Find the value of

Find 

Show that 

and 

Circle the expression for

Circle the expression for

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.

The functions  and  are such that

where  and  are constants.

Find the value of  and the value 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 

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.