how can you find the domain and what would it beSolutionSoul

how can you find the domain and what would it be?

Soultion :

Domain is the points where function is defined

since function has power of cuberoot root therefore negative value inside the cube root is acceptable here

and function difined for all positive and negative real number

but as we can see inside the cubic root function has got 36-x² in its denominator therefore

any fraction (rational ) number is defined as p/q where q is not equal to 0

36-x^2 =0 is not the domian of the function

x = +/-6 is not the domain

thus

Domain of given function = All real number except +/-6 = R - {+/-6}