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  4. The sum of all real numbers which are not in the range of f(x)=(x2-3 x+2/x2-4 x+3) is equal to

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Q. The sum of all real numbers which are not in the range of $f(x)=\frac{x^2-3 x+2}{x^2-4 x+3}$ is equal to

Relations and Functions - Part 2

Solution:

$f(x)=\frac{(x-1)(x-2)}{(x-3)(x-1)}=\frac{x-2}{x-3}, x \neq 1,3$
Domain of function $=R-\{1,3\}$.
Range of function $=R-\left\{\frac{1}{2}, 1\right\}$