Question

If $f\left(x\right)=\frac{x^3+3x+5}{x^2-3x+2}$. Discuss the continuity of $f\left(x\right)$ on $\left[0,5\right]$.

Answer 1

Consider the given function.

$f\left(x\right)=\frac{x^2+3x+5}{x^2-3x+2}$

$f\left(x\right)=\frac{x^2+3x+5}{(x-1)(x-2)}$

Since, the denominator of $f\left(x\right)$ is equal to $0$, at $x=1$ and $x=2$, the function is discontinuous at $x=1$ and $x=2$.

Thus, the function $f\left(x\right)$ is discontinuous at two points in $[0,5]$.