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# Functions

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.

 Related Calculators Calculator Functions Calculate Exponential Function Calculate Inverse Function calculating gamma function

## Types of Functions

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.

Polynomial

Linear functions:

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

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

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.

Solution:

x2 + 7 = 11

x2 = 11 – 7

x2 = 4

x = 2

Example problem 2: Functions

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

Solution:

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