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Indeterminate value in functions

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Indeterminate Value in Functions

 »  Functions evaluate to 0000
    →  eg: x2-4x-2x=2=00x24x2x=2=00

Though the function evaluates to 0000, it may take a value.

evaluating a function

Consider the value of function f(x)=x2-1x-1f(x)=x21x1 when x=2.2x=2.2.

On substituting x=2.2, we get f(2.2)=2.22-12.2-1.

function evaluating to 0/0

Consider the value of function f(x)=x2-1x-1 when x=1

On substituting x=1, we get

That is, the function evaluates to indeterminate value when x=1.

Let us closely examine the function f(x)=x2-1x-1.

The numerator be factorized as x2-1=(x+1)(x-1)

Rewriting the function f(x)=x2-1x-1 as the function f(x)=(x+1)(x-1)x-1.

It is noted that the function can be simplified to f(x)=x+1 when x1. Note that 0 cannot be canceled out in expressions or equations.

So the given function
    =x+1 when x1
    =x2-1x-1 when x=1

By this it is concluded that f(x)x=1 is indeterminate value 00.

Many students wrongly understand that the algebraic simplification (like canceling x-1 in the example above) solves the indeterminate value. It is not so -- the function remains indeterminate at that input value x=1.

another example

Given f(x)=x3-8x2-4 What is f(2)?

The answer is '00'


Function evaluates to indeterminate value: Function f(x) evaluates to indeterminate value for x=a if f(a)=00.


The outline of material to learn "limits (calculus)" is as follows.

Note : click here for detailed outline of Limits(Calculus).

    →   Indeterminate and Undefined

    →   Indeterminate value in Functions

    →   Expected Value

    →   Continuity

    →   Definition by Limits

    →   Geometrical Explanation for Limits

    →   Limit with Numerator and Denominator

    →   Limits of Ratios - Examples

    →   L'hospital Rule

    →   Examining a function

    →   Algebra of Limits

    →   Limit of a Polynomial

    →   Limit of Ratio of Zeros

    →   Limit of ratio of infinities

    →   limit of Binomial

    →   Limit of Non-algebraic Functions