Question

The domain of the function 5cos-1 2x/3 is

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{f(x)=5\,cos^{-1}\left(\dfrac{2x}{3}\right)}$

Now, f(x) is defined, if and only if

$\sf{-1\le\dfrac{2x}{3}\le1}$

$\sf{\implies-3\le2x\le3}$

$\sf{\implies-\dfrac{3}{2}\le\,x\le\dfrac{3}{2}}$

$\sf{Hence,\,\,\,dom(f)\in\left[-\dfrac{3}{2},\dfrac{3}{2}\right]}$