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

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We are given f(x) = 2x and g(x) = sin x.

Now f (g(x))

= f (sin x) = 2sin x.

Now sin x can take all values in the set [-1, 1]

2*sin x can take all values in the set [-2, 2].

**Therefore the range of f (g(x)) for f(x) = 2x and g(x) = sin x is [-2, 2].**

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).