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Books and other education websites provide "matter-of-fact" knowledge. Instead, nubtrek provides a thought-process to discover knowledge.

In each of the topic, the outline of the thought-process, for that topic, is provided for learners and educators.

Read in the blogs more about the unique learning experience at nubtrek.continue

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Indeterminate Value in Functions

» Functions evaluate to `0/0`

→ eg: `(x^2-4)/(x-2)|_(x=2) = 0/0`

*plain and simple summary*

nub

*plain and simple summary*

nub

dummy

Functions can evaluate to indeterminate value `0/0` at some input values.

*simple steps to build the foundation*

trek

*simple steps to build the foundation*

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Some functions evaluate to indeterminate value at some input values. This is illustrated with an example.

Starting on learning "indeterminate value in functions". ;; Some functions evaluate to indeterminate value at some input values. This is illustrated with an example.

What is the value of `f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1)` when `x=2.2`?

- `0/0`
- indeterminate value
- `3.2`

The answer is '`3.2`'. On substituting `x=2.2`, we get `f(2.2)= color(deepskyblue)(2.2^2-1)/color(coral)(2.2-1)`.

What is the value of `f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1)` when `x=1`?

- `0/0`
- indeterminate value
- both the above

The answer is 'Both the above'. On substituting `x=1`, we get

`f(1)`

`quad quad =color(deepskyblue)(1^2-1)/color(coral)(1-1)`

`quad quad = color(deepskyblue)(0)/color(coral)(0)`.

Let us closely examine the function `f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1)`. Can the numerator be factorized?

- Yes, `x^2-1 = (x+1)(x-1)`
- Cannot be factorized as Factorization is only for numbers, not for algebraic expressions

The answer is 'Yes - `x^2-1 = (x+1)(x-1)`'.

Rewriting the function `f(x) = color(deepskyblue)(x^2-1)/color(coral)(x-1)` as the function `f(x) = color(deepskyblue)((x+1)(x-1))/color(coral)(x-1)`. Can the function be simplified?

- Simplified to `f(x)= x+1`
- Simplified only when `x!=1` to `f(x)= x+1`

The answer is 'Simplified to `f(x)= x+1` when `x!=1`'. Note that `0` cannot be canceled out in expressions or equations.

So the given function

`f(x)`

`quad quad = x+1 ` when `x!=1`

`quad quad = (x^2-1)/(x-1) ` when `x=1`

By this it is concluded that `f(x)|_(x=1)` is indeterminate value `0/0`.

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`.

*comprehensive information for quick review*

Jogger

*comprehensive information for quick review*

Jogger

dummy

** Function evaluates to indeterminate value: ** Function `f(x)` evaluates to indeterminate value for `x=a` if `f(a) = 0/0`.

*practice questions to master the knowledge*

Exercise

*practice questions to master the knowledge*

Exercise

Given `f(x)=(x^3-8)/(x^2-4)` What is `f(2)`?

- `0/0`
- `10`
- `1`

The answer is '`0/0`'

*your progress details*

Progress

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Progress

What is the value of f of x equals x squared minus 1 by x minus 1 when x equals 2 point 2?

0

0 by 0

indeterminate;value

indeterminate value

3;point;2;3.2

3 point 2

The answer is "3 point 2". On substituting x equals 2. point 2, we get f of 2 point 2 equals 2 point 2 squared minus 1 by 2 point 2 minus 1.

What is the value of f of x equals x squared minus 1 by x minus 1 when x equals 1?

0

0 by 0

indeterminate;value

indeterminate value

both;above

both the above

The answer is "Both the Above". On substituting x=1, we get ;; f of 1 ; equals 1 squared minus 1 by 1 minus 1 ;; equals 0 by 0.

Let us closely examine the function f of x equals x squared minus 1 by x minus 1. Can the numerator be factorized?

yes;s;squared;minus;1

yes; x squared minus 1 equals x plus 1 multiplied x minus 1

cannot;be;factorized;not;only

Cannot be factorized as Factorization is only for numbers, not for algebraic expressions

The answer is "Yes; x squared minus 1 equals x plus 1 multiplied x minus 1"

Rewriting the function f of x equals x squared minus 1 by x minus 1 as the function ;; f of x equals x + 1 multiplied x minus 1 divided by x minus 1. ;; Can the function be simplified?

simplified to; simplified 2

Simplified to f of x equals x + 1

only;when;not;equal;1

simplified only when x not equal 1 to f of x equals x + 1

The answer is "simplified only when x not equal 1 to f of x equals x + 1". Note that 0 cannot be canceled out in expressions or equations.

So the given function ;; f of x ;; equals x + 1 when x not equals 1 ;; and x squared minus 1 by x minus 1 when x equals 1 ;; By this it is concluded that f of x at x =1 is indeterminate value 0 by 0.;; Many students wrongly understand that the algebraic simplified, like canceling x minus 1 in the example above, solves the indeterminate value. It is not so, The function remains indeterminate at that input value x equals 1.

Functions can evaluate to indeterminate value 0/0 at some input values.

Function evaluates to indeterminate value: Function f of x evaluates to indeterminate value for x equals a if f of a equals 0 by 0.

Given f of x equal x cube minus 8 by x squared minus 4. What is f of 2?

0

0 by 0

10

10

1

1

The answer is "0 by 0"