Question

Give the domain and range of the relation
$y=\frac{-6}{x-2}$

• A. domain: $(-\infty ,-2)\cup (2,\infty )$; range: $(-\infty ,\infty )$
• B. domain: $(-\infty ,2)\cup (2,\infty )$; range: $(-\infty ,\infty )$
• C. domain: $(-\infty ,2)\cup (2,\infty )$; range: $(-\infty ,0)\cup (0,\infty )$
• D. domain: $(-\infty ,-2)\cup (-2,\infty )$; range: $(-\infty ,0)\cup (0,\infty )$

Answer 1

The correct option is C domain: $(-\infty ,2)\cup (2,\infty )$; range: $(-\infty ,0)\cup (0,\infty )$

The function is only undefined when $x-2=0\Rightarrow x=2$

Hence domain is $x\in R-\left\{2\right\}$

Also $xy=2y-6$

$\Rightarrow x=\frac{2y-6}{y}$

Clearly y can take all values except for 0.

Hence range is $x\in R-\left\{0\right\}$