Find the points of discontinuity, if any, of the following function: `f(x)={x^(10)-1\ \ \ ,\ \ \ if\ xlt=1x^2\ \ \ ,\ \ \ if\ x >1`

Explanation

The given function `f` is `f(x)= x^{10}-1, text { if } x leq 1 x^{2}, text { if } x>`


The given function `f` is defined at all the points of the real line.


Let `c` be a point on the real line.


Case I:


If `c<1`, then `f(c)=c^{10}-1` and `lim _{x -> infty} f(x)=lim _{x -> infty}(x^{10}-1)=c^{10}-1`


`therefore lim _{x -> c} f(x)=f(c)`


Therefore, `f` is continuous at all points `x`, such that `x<1`


Case II:


...