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Students can learn about Functions and work problems associated with them. They can get the help of the online Math tutors in understanding the concepts clearly.

Here we are going to see about the functions and their types in following below.

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Types of Functions

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Some of the types of functions are following below,

  • Inverse functions
  • Composite functions
  • Odd and even functions
  • Polynomial - Linear, Quadratic, Cubic functions
  • Exponential and logarithmic functions
  • Monotonic functions
  • Periodic functions

Inverse functions:

If a function f (m) is, then its function of inverse is f-1(m).

            f-1 (m) = 1/f (m)

Composite functions:

There are two functions combined.

Example of composite function,

            (f.h) (m) = f (h (m))

            (h.f) (m) = h (f (m))

Even and odd functions:

An even function has real variable.

f (m) = f (-m)

Example: |m|, m2 and so on.

Real variables present in the odd function.

-f (m) = f (-m)

f (m) + f (-m) = 0

Example: m, m3, and so on.


Linear functions:

The function that f (m) = am + b, where a and b are constants, where am + b = 0 is called as linear function.

Quadratic functions:

A function that f (m) = am2 + bm +c, where a, b and c are constants called as quadratic function.

Cubic functions:

A function that f (m) =am3 + bm 2 + cm + d, where a, b, c and d are constants called as cubic function.

Monotonic functions:

A function that moves in only one direction called as monotonic function.

Example: f (m) = cos (m) + 4.

Periodic functions:

A function that repeats over particular interval of time called periodic function.

 Example: sin (m), cos (m).

Exponential and logarithmic functions:

A function that f(m) = em, e is unequal to zero called as exponential form function.

A function that inverse of exponential called as exponential function.

  f (m) = log2(m)

Solving Functions

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Students can learn How to solve functions from the solved examples. Here are some examples:

Example problem 1: Functions

Find out the value of x if g (x) = 11 where g (x) = x2 + 7.


x2 + 7 = 11

x2 = 11 – 7

x2 = 4

x = 2

Answer:  x = 2.

Example problem 2: Functions

Find out the function f (x) = x3 – 17, if the value of x is 1, 2 and 3.


f (x) = x3 – 17

when  x=1

f (1) = (1)3 – 17

        = 1 –1 7

        = -16

when x = 2

f (2) = (2)3 – 17

        = 8 – 17

        = 9

when x = 3

f (3) = (3)3 – 17

        = 27 – 17

        = 10

The correct answer is

x =1; f(x) = -16

x =2; f(x) = 9

x =3; f(x) = 10

Students can alos get help with Algbera homework problems involving Functions from the online tutors.

More topics in  Functions
Types of Functions Period of a Function
Domain and Range of a Function Vertical Line Test
Graphing Functions
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