Question

If $f\left(x\right)=\frac{x^2+2}{x-1}$ when $x<3$, $f\left(x\right)=\frac{\sin x}{x-3}$ when $x>3$, for what values of x is the function not defined

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

Answer: (A)

3

$f\left(x\right)=\frac{x^2+2}{x-1}$ for $x<3,x\ne 1$

and
$f\left(x\right)=\frac{sin\left(x\right)}{x-3}$ for $x>3,x\ne 3$.

Hence $f\left(x\right)$ is not defined for $x=1,3$.