The domain of the function $f(x)=\frac{\sqrt{2x-1}+\sqrt{4x+7}}{\sqrt{4-x}+\sqrt{3+17x+1}}$ is:

\(\begin{bmatrix}-\frac{7}{4},\frac{1}{2}\end{bmatrix}\) \(\begin{bmatrix}\frac{-3}{17},\frac{1}{2}\end{bmatrix}\) \(\begin{bmatrix}\frac{-3}{17},4\end{bmatrix}\) \(\begin{bmatrix}\frac{1}{2},4\end{bmatrix}\)

\(\begin{bmatrix}\frac{1}{2},4\end{bmatrix}\)

For domain:- 2x - 1 ≥ 0 ⇒ $x≥\frac{1}{2}$ 4x + 7 ≥ 0 ⇒ $x≥\frac{-7}{4}$ 4 - x ≥ 0 ⇒ x ≤ 4 4 + 17x ≥ 0 ⇒ $x≥\frac{-4}{17}$ Combining the equations, $x≥\frac{1}{2}$ & x < 4 $[\frac{1}{2},4]$