Question

$f\left(x\right)=\sqrt{x+1}\&g\left(x\right)=2x-3$

Find the domain of $\frac{f}{g}$

• A. $R-\left\{\frac{3}{2}\right\}$
• B. $(-1,\infty )-\left\{\frac{3}{2}\right\}$
• C. $[-1,\infty )-\left\{\frac{3}{2}\right\}$
• D. $(-1,\infty )$

Answer 1

The correct option is C

$[-1,\infty )-\left\{\frac{3}{2}\right\}$

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

$x+1\ge 0\Rightarrow x\ge -1$

$Also,2x-3\ne 1$

$\Rightarrow x\ne \frac{3}{2}$