Multiple Value Function

During mathematics, a multivalued function is an overall relation; specifically all input is related with one or else further outputs. Exactingly words, a well-defined function connections one, also only one, output toward at all particular input. The word "multiple value function" is, consequently, a misnomer while functions be single-valued.Multiple value functions frequently occur as of functions are not injective. Such functions perform not contain an inverse function, except they perform include an inverse relation. It is also called the set-valued function.

Examples for multiple value function

 

This figure do not symbolize a right function since the element 3 within x be related through two elements b with c within y.

Each real number larger than zero or else each complex numbers except for 0 have two square roots. The square roots of 9 be in the set {+3,−3}.

The square roots of 0 be describe through the multiset {0,0}, since 0 be a root of multiplicity 2 of the polynomial x².

Every complex number include three cube roots

Complex logarithm functions are multiple-valued. The values implicit with log (1) be 2πni for every integers n.

Inverse trigonometric function is multiple-valued since trigonometric function is periodic.

tan(π/4)=tan((5π/4)=tan((-3π/4)=tan(2(n+1)π/4)=...1

Therefore arctan(1) might be consideration of since contain multiple values such as π/4, 5π/4, −3π/4, and rapidly. We know how to treat arctan since a single-valued function through restrict the domain of to -π/2 < x < π/2. Therefore, the range of arctan(x) becomes -π/2 < x < π/2. These values as of a limited field are call principal values.

Example problems

Problem 1
Given function f(x)=7x-5, what is the value of f(1) and(f(2)?
solution:

Given function f(x)=7x-5)

We can  find the value of f(1), to substitute 1 for the given function,

f(1)=7x1-5

      =7-5

f(1)=2

We can  find the value of f(2), to substitute 2 for the given function,

f(2)=7x2-5

      =14-5

f(2)=9

Problem 2
Given function f(x)=5x²+6x-5, what is the value of f(5)?
solution:

Given function f(x)=5x²+6x-5

We can  find the value of f(5), to substitute 5 for the given function,

f(5)=5x5²+6x5-5

      =5x25+6x5-5

     =125+30-5

  f(5)=150