Write Given f(x)=2−4x−−−−−√ and g(x)=−3x, find the following: a. (g∘f)(x) the domain and range of the function using interval notation.

If we have two functions g(x) and f(x)

I suppose that the functions here are:

f(x) = 2 - √(4*x)

g(x) = -3*x

First, let's analyze the functions:

g(x) as not any problem for any value of x, so the domain is the set of all the real numbers.

f(x) has a square root on it, and we know that the square root of a negative number is equal to a complex number, so here we can not have negative values of x.

The domain of f is D = x ∈ {0, ∞}

Then (gof)(x) = g(f(x)) = -3*(2 - √(4*x)) = -6 + 3*√(4*x)

We can see that g(x) does not have any problem, and the problems with f(x) remain there, so the domain of the composition is equal to the domain of f(x):

D =  x ∈ {0, ∞}