continuous formula

[jsmviper22]

give a formula for the extended function f(x)= (x^3-4x^2-11x+30)/(x^2-4)

 

[soroban]

Jello, jsmviper22!

Give a formula for the extended function f(x) = (x³ - 4x² - 11x + 30)/(x² - 4)
.

Sorry, I don't understand (and I've spoken English for over 70 years).

What is an "extended function"? . . . And what does "give a formula" mean?

 

[jsmviper22]

im sorry i forgot to add at the end (that is a continuous everywhere)

 

[stapel]

Okay, but you haven't answered the question: What is the definition of an "extended" function?

Eliz.

 

[pka]

Note that x<SUP>3</SUP>−4x<SUP>2</SUP>−11x+30 factors as (x−2)(x−5)(x+3).
And x<SUP>2</SUP>−4 factors as (x−2)(x+2).
Therefore x=2 is a removable discontinuity, whereas x=−2 is an essential discontinuity.
This means that one can extend the function’s definition to make it continuous at x=2.
However, it is impossible to make it continuous everywhere.