Question

The sum of all real numbers which are not in the range of $f\left(x\right)=\frac{\left(x-1\right)\left(x-2\right)}{\left(x-3\right)\left(x-1\right)}$ is equal to

• A. $\frac{3}{2}$
• B. $\frac{1}{2}$
• C. $1$
• D. $\frac{5}{2}$

Answer 1

The correct option is B $\frac{1}{2}$

The sum of all real number which are not in range of $f\left(x\right)=\frac{(x-1)(x-2)}{(x-3)(x-1)}$ is equal to

Domain: $(-\infty ,1)\cup (1,3)\cup (3,\infty )$

Range: $(-\infty ,1)\cup (1,\infty )$

Sum of all reals number which are not in range os $(0+(-1\left)\right)=-1$

$(x-3)=0;(x-1)=0$

$x=3x=1$

Domain $=R-\{1,3\}$