Question

Use the function composition calculator to find the domain of (f ∘ g)(x), where f(x) = √(4 - x) and g(x) = 3x - 2.

a) x ≤ 4/3
b) x ≥ 4/3
c) x ≤ 2
d) x ≥ 2

Answer 1

To find the domain of (f ∘ g)(x), evaluate the domains of f(x) and g(x) and find the values of x for which both are defined. The domain of (f ∘ g)(x) is x ≤ 4/3.

Step-by-step explanation:

To find the domain of (f ∘ g)(x), we need to consider the domain of the composite function.

The composite function (f ∘ g)(x) represents the function f(g(x)).

So, we need to find the values of x for which both f(x) and g(x) are defined.

Let's start with the domain of g(x). Since g(x) is a linear function, it is defined for all real numbers.

Next, let's consider the domain of f(g(x)), which is the domain of f(x) such that g(x) is within its domain.

The function f(x) = √(4 - x) is defined only when the expression inside the square root is non-negative.

So, we need to find the values of x for which 4 - x ≥ 0.

Simplifying the inequality, we get x ≤ 4.

Therefore, the domain of (f ∘ g)(x) is x ≤ 4/3.