How to define

Let’s first understand the definition of function. I’ll keep it simple. Basically, function is like a manufacturing unit/industry; like in case of a manufacturing unit or an industry we give raw material as an input and we get finished products as an output, the same things happens with function also; you give an input value to the function you get an output.

For example: Let’s say I have a function f(x) = 2x+8 (a linear function with respect to x).

If I put different values of x in the expression, I’ll get different output values. Let’s take few values such as

x = -1 for which f(x) = 6,

x = 0 for which f(x) = 8,

x = 1 for which f(x) = 10.

Keep the image below deeply embedded in your mind and functions will not be an issue for you.            

Values of x are known as input values and values of f(x) are known as output value.

Now you may have any function, for example;

1. Linear Function
2. Quadratic Function
3. Logarithmic Function
4. Exponential Function

So, on and so forth.

Every function basically performs only one job that is you give it an input value and it will give you corresponding output value.

Questions from this chapter can be as easy as;

If a function f(x) is defined as f(x) = (x-1)/x, then find the value of f(1) + f(2) + f(3) + f(4)?

Now in this question we need to figure out the values of f(1), f(2), f(3) and f(4).

f(1) = 0/1 = 0

f(2) = 1/2

f(3) = 2/3

f(4) = 3/4

Hence final answer will be 0 + 1/2 + 2/3 + 3/4 = 23/12.

Other type of questions can be related to domain and range. Let’s say suppose you face a question;

f(x) = (x+2) / (x-3)

In the above function, for what value of x is the function f(x) is undefined?

Now, what we need to understand in this question is that if I put x = 3, I’ll get the value of f(x) = 5/0 which is not defined in math. Or in other terms, I can say that for input value of x = 3, the function f(x) is not defined.

And, hence comes the topic ‘Domain and Range’.

So, what is domain and what is range?

Domain is the set of input values for which function is defined. So, in the above case I can say that domain is all real values apart from x = 3.

And the output values obtained for corresponding input value is known as range. Hence in this case we have range as all real values.

One more thing we need to understand is the term “root”. So, basically what is root of a function.

Go back to the basics of ‘what is function’?

What you’ll realize is it’s all about giving an input value and getting an output value.

Now, coming back to roots: Roots are those input values for which output value is equal to 0. Have a look at the below example.

Last concept for the basics of function is “complex function”.

Let me make you understand that with the help of a process diagram.

Consider two functions; f(x) = 2x+3 and g(x) = 3x/7. We need to find the value of g(f(2)).

Read the process graph below and you’ll understand what is meant by complex function. It’s about finding the output value of one function and considering it as an input for another.

Hence, in short complex function is nothing but combination of two or more functions.

Watch the below video in order to have more in-depth understanding of functions-basics.

Space for YouTube video

Try the below questions once you have gone through the above video;