Question

The domain of the function $f\left(x\right)=\sqrt{4x-3}+\sqrt{2x-6}$ is

• A. $[3,\infty ]$
• B. $[\frac{3}{4},\infty ]$
• C. $[\frac{4}{3},\infty ]$
• D. $[2,\infty ]$

Answer 1

The correct option is A $[3,\infty ]$

$f\left(x\right)=\sqrt{4x-3}+\sqrt{2x-6}$

• $4x-3\ge 04x\ge 3\Rightarrow x\ge \frac{3}{4}\Rightarrow x\in [\frac{3}{4},\infty ).....\left(1\right)$
• $2x-6\ge 02x\ge 6\Rightarrow x\ge 3\Rightarrow x\in [3,\infty ).....\left(2\right)$

From equation $\left(1\right)$ and $\left(2\right)$, we get

$x\in [\frac{3}{4},\infty )\cap [3,\infty )$

$\Rightarrow x\in [3,\infty )$