Find the domain of the variable x for which the following equations determine y as a real function of x.

If G(x)= sin 2x, find G(0),G(1/4 pie),and G(7/8 pie)

can someone help me please!

just look at the graph of sin(x). Clearly, it is defined everywhere, so its domain is all real numbers.

sin(2x) gets to each x value twice as fast, but has exactly the same domain: all real numbers.

To find the domain of the variable x for which the equation determines y as a real function of x, we need to determine the values of x for which the equation is valid.

In this case, the equation is G(x) = sin 2x. The sine function is defined for all real numbers, so there are no restrictions on the domain of x. Therefore, the domain of x is (-∞, ∞) or all real numbers.

Now, let's find G(0), G(1/4 π), and G(7/8 π).

To find G(0), substitute x = 0 into the equation G(x) = sin 2x:
G(0) = sin 2(0) = sin 0 = 0.

To find G(1/4 π), substitute x = 1/4 π into the equation G(x) = sin 2x:
G(1/4 π) = sin 2(1/4 π) = sin (1/2 π) = sin (π/2) = 1.

To find G(7/8 π), substitute x = 7/8 π into the equation G(x) = sin 2x:
G(7/8 π) = sin 2(7/8 π) = sin (7/4 π) = sin (3π/2) = -1.

Therefore, G(0) = 0, G(1/4 π) = 1, and G(7/8 π) = -1.