Precalc Question

Question

Let y = f(z) = √ 4 − z 2 and z = g(x) = 2x + 3. Compute the composition y = f(g(x)). Find the largest possible domain of x-values so that the composition y = f(g(x)) is defined.

Answer 1

I assume you mean y = f(z) = √ 4 − z² If not, it should have been written as 2z.

"f(g(x))" means that we apply the "g" function to x, and then apply the "f" function to the result. The equivalent definition is that we replace x in f(x) with the results of g(x).

So....y = f(g(x)) = √4 - (2x + 3)²

(expand and simplify to taste....)