Question

If $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=2x-3$, then domain of (fog) (x) is

• A. $(-\infty ,-3)$
• B. $(-\infty ,\frac{-3}{2})$
• C. $[-\frac{3}{2},0]$
• D. $[0,\frac{3}{2}]$
• E. $[\frac{3}{2},\infty )$

Answer 1

Answer: (E)

$[\frac{3}{2},\infty )$

Given, $f\left(x\right)=\sqrt{x}$ and $g\left(x\right)=2x-3$
$\therefore \left(fog\right)\left(x\right)=f\left\{g\right(x\left)\right\}=f\{2x-3\}=\sqrt{2x-3}$
For domain of (fog)(x),
$2x-3\ge 0\Rightarrow 2x\ge 3\Rightarrow x\ge \frac{3}{2}$
Therefore, $x\epsilon [\frac{3}{2},\infty )$