Domain of the function f(x) = frac{x^2 - 3x + | vedclass

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(D) The given function is $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$.Factorizing the numerator: $x^2 - 3x + 2 = (x - 2)(x - 1)$.Factorizing the denomin

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$\{x : x \in R, x 
eq 2, x 
eq -3\}$

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(D) The given function is $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$.Factorizing the numerator: $x^2 - 3x + 2 = (x - 2)(x - 1)$.Factorizing the denominator: $x^2 + x - 6 = (x + 3)(x - 2)$.Thus,$f(x) = \frac{(x - 2)(x - 1)}{(x + 3)(x - 2)}$.The function is defined for all real values of $x$ except where the denominator is zero.Setting the denominator to zero: $(x + 3)(x - 2) = 0$,which gives $x = -3$ or $x = 2$.Therefore,the domain of the function is the set of all real numbers except $2$ and $-3$.Domain = $\{x : x \in R, x 
eq 2, x 
eq -3\}$.

Column $I$	Column $II$
$(A)$ If $-1 < x < 1$,then $f(x)$ satisfies	$(p)$ $0 < f(x) < 1$
$(B)$ If $1 < x < 2$,then $f(x)$ satisfies	$(q)$ $f(x) < 0$
$(C)$ If $3 < x < 5$,then $f(x)$ satisfies	$(r)$ $f(x) > 0$
$(D)$ If $x > 5$,then $f(x)$ satisfies	$(s)$ $f(x) < 1$

Domain of the function $f(x) = \frac{x^2 - 3x + 2}{x^2 + x - 6}$ is

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