The question is to find the solution to and domain of fgx an

The question is to find the solution to and domain of f(g(x)) and g(f(x)) where f(x) =sin 2x and g(x) = 1/x. I\'m confused. I think the answers are f(g(x)) = sin 2/x and g(f(x)) = 1/sin 2x and the domain being any points which would cause the denominator to be zero. But, that seems way too easy. What am I missing?

You aint missing anything :P
For sinx, x lies between -pi/2 to pi/2

so, for sin(2/x) , 2/x lies between -pi/2 to pi/2

or, 1/x lies between -pi/4 to pi/4

or, x lies between -4/pi to 4/pi excluding 0

For 1/x, domain is R-{0}

So, for 1/sin2x, sin2x not =0

and for sin2x, domain is -pi/4 to pi/4

So, domain will be -pi/4 to pi/4 excluding 0

$The question is to find the solution to and domain of f(g(x)) and g(f(x)) where f(x) =sin 2x and g(x) = 1/x. I\'m confused. I think the answers are f(g(x)) = si$

The question is to find the solution to and domain of fgx an

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