If the relation f is defined by $f (x) = {\begin{matrix} x^{2}, & 0 \leq x \leq 3 3 x, & 3 \leq x \leq 10 \end{matrix}$
and the relation g is defined by $g (x) = {\begin{matrix} x^{2}, & 0 \leq x \leq 2 3 x, & 2 \leq x \leq 10 \end{matrix}$
then,

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If LCM of f(x) and g(x) is 6x2+13x+6, then which of the following cannot be the HCF of f(x) and g(x) ?

The correct option is B 3x+1LCM of f(x) and g(x) = 6x2+13x+6=(2x+3)(3x+2).We know that, HCF is a factor of LCM.Therefore, 3x+1 cannot be the HCF.

If LCM of f(x) and g(x) is $6 x^{2} + 13 x + 6$ , then which of the following cannot be the HCF of f(x) and g(x) ?

The correct option is B 3x+1
LCM of f(x) and g(x) = $6 x^{2} + 13 x + 6 = (2 x + 3) (3 x + 2)$ .
We know that, HCF is a factor of LCM.
Therefore, $3 x + 1$ cannot be the HCF.