Question

Examine the following functions for continuity :

$f(\times )=\frac{{\times }^2-25}{\times +5},x\times not=-5$

Answer 1

$f(\times )=\frac{{\times }^2-25}{\times +5}=\frac{(\times +5)(\times -5)}{(\times +5)}=\times -5$

$\therefore f(\times )=\times -5$ is a polynomial function, so f(x) is continuous at all values of x.

Note In any rational function $f\left(x\right)=\frac{p\left(x\right)}{q\left(x\right)}$ and if P(x) and q(x) are polynomials and q(x) is zero at any value of x and p(x) = 0, then f(x) is not continuous at that point.