Find the points of discontinuity, if any, of the following function: `f(x)={(x^4-16)/(x-2)\ \ \ ,\ \ \ if\ x!=2 16\ \ \ ,\ \ \ if\ x=2`

Explanation

Given: `f(x)= frac{x^{4}-16}{x-2}, text { if } x neq 2 16, text { if } x=2`


When `x neq 2` then



`f(x)=frac{x^{4}-16}{x-2}=frac{x^{4}-2^{4}}{x-2}=frac{(x^{2}+4)(x-2)(x+2)}{x-2}=(x^{2}+4)(x+2)`



We know that a polynomial function is everywhere continuous.


Therefore, the functions `(x^{2}+4)` and `(x+2)` are everywhere continuous.


So, the product function `(x^{2}+4)(x+2)` is everywhere continuous.


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