Question

The domain of the function $f\left(x\right)={\sin }^{-1}\left(\frac{2x-1}{3x-2}\right)+{\cos }^{-1}\left(\frac{3x-4}{5}\right)$ is

• A. $\left[1,3\right]$
• B. $\left[-\frac{1}{3},3\right]$
• C. $\left[-\frac{1}{3},\frac{3}{5}\right]\cup \left[-\frac{1}{3},0\right]$
• D. $\left[-\frac{1}{3},0\right]$

Answer 1

The correct option is A $\left[1,3\right]$

$F\left(x\right)={\sin }^{-1}\left(\frac{2x-1}{3x-2}\right)+{\cos }^{-1}\left(\frac{3x-4}{5}\right)$

Now,

$3x-2\ne 0$

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

$-1⩽\frac{3x-4}{5}⩽1$

$\Rightarrow -5⩽3x-4⩽5$

$-\frac{}{}$