GRE Algebra | Functions

An algebraic expression consist one variable is used to define a function of that variable. For example, the expression 2y – 7 can be used to define a function f by,

f(y) = 2y - 7 

where f(y) is called the value of f at y and function value can be obtained by putting the value of y in above expression.If y=1, then f(1) is

f(1) = 2(1) - 7
f(1) = -5 

Hence, the value of f(1) is -5.

For each input value of y, the function f(y) gives exactly one output.So, it can be say that function f act as a machine which takes an input of the variable y and produces the corresponding output.

It might be possible sometimes when more than one value of y can give the same output of f(y). For example:



f(x) = 2x2 - 4x + 7

Put (x = 0)
f(0) = 2(0) - 4(0) + 7 
     = 7

Put (x = 2)
f(2) = 2(2)2 - 4(2) + 7
     = 8 - 8 + 7
     = 7 

Hence, for both values of x = 0, 2 f(x) gives the same output.

Domain of a function is the set of all the permissible inputs. For example:

g(y) = √(x-5) is function.
√(x-5) ≥ 0
x ≥ 5 

Here, domain of the function is [5, ∞)

  • Example-1: Let f be the function defined by f(x)= 3x/(x2 – 4).Find the domain.
    Solution:

    Let f(x) = 0 then
    3x/x2 - 4 = 0
    
    Put (x=2) 
    3(2)/22 - 4 = 0
    6/(4-4) = 0
    
    Put (x= -2) 
    3(-2)/22 - 4  = 0   
    6/(4-4) = 0  

    Here, f is not defined at (x = 2 and x = -2) because 6/0 is not defined.
    Hence, the domain of f consists of all real numbers except 2 and -2.

  • Example-2: Let f be the function defined by g(x) = √(x – 3) + 11. Find the domain.
    Solution:

    √(x - 3) + 11 = 0 

    In this case if x < 3, then g(x) is not a real number.
    Hence, domain of g consists of all the real numbers x such that x ≥ 3.



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.




Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.