Relations and Functions — MATHS STD 11 Science — Question

1. $\big[-1,2\big)\cap\big[3,\infty\big)$

Solution:

$\text{f(x)}=\sqrt{\frac{(\text{x}+1)(\text{x}-3)}{\text{x}-2}}$

For f(x) to be defined,

$(\text{x}-2)\neq0$

$\Rightarrow\text{x}\neq2\ ...(\text{i})$

Also,

$\frac{(\text{x}+1)(\text{x}-3)}{\text{x}-2}\geq0$

$\Rightarrow\frac{(\text{x}+1)(\text{x}-3)(\text{x}-2)}{(\text{x}-2)^2}\geq0$

$\Rightarrow(\text{x}+1)(\text{x}-3)(\text{x}-2)\geq0$

$\Rightarrow\text{x}\in\big[-1,2\big)\cup\big[3,\infty\big)\ ...(\text{ii})$

From (i) and (ii),

$\text{x}\in\big[-1,2\big)\cap\big[3,\infty\big)$