Domain and Range

I am often asked what is the domain and range of a function. So in the following tutorials I introduce you to this concept by looking at linear, quadratic, root and reciprocal functions.

Tutorial on linear and quadratic functions

Tutorial on square root and reciprocal functions

Combining Functions

You will be asked to combine functions. In the first of these tutorials you are shown what we mean by combining functions and introduced to a simple example and the notation that you may expect to see.

Tutorial on Combining Functions

You may like to try the following examples where I combine two functions and introduce combining three functions.

Worked Solutions to (1) (2) and (3)

 

In these examples I have introduced exponential and log types for you to try. Aim to simplify the answers as well.

Worked Solutions to (4) (5) and (6)

 

Inverse Functions

If you are not sure what an inverse function is or how to find one then this video should show you.

You will be shown how to find the inverse of this function.

Tutorial on finding Inverse Functions

 

I would now recommend that you try the following examples.

In this example the aim is to have two x values in the function and show that you can use other letters other than f(x)

(1)

Worked solution to (1)

 

In the next example you are given an exponential function and introduced to using other notation.

(2)

Worked solution to (2)

 

Finally an example using natural logs.

(3)

Worked solution to (3)

 

Further Mixed Examples

Here are two examples which you may like to try before looking at the video.

 

(1)

 

Tutorial and Worked solution to (1)

 

(2)

 

Tutorial and Worked solution to (2)