If f(x) = 2x and g(x) = sin x, what is the range of f (g(x))?

f(x) = 2x and g(x) = sin x, To find the range of f
(g(x)).

f(g(x)) =
2*(x).

=> f(g(x)) =
2sinx.

Therefore the range of f(g(x)) is the range of
2sinx. Or the range of 2sinx is the set of all values 2sinx can
take.

Since sinx is a continous function bounded function
within -1 to +1. f(g(x)) = 2sinx can take all the values from -2 to
2.

So the range of f(g(x)) = 2sinx is the set of all values
in the closed interval (-2 , 2).