How do you find the composite function (f ∘ g)(x) for f(x) = sqrt(x) and g(x) = x + 4?

To find the composite function (f ∘ g)(x), substitute g(x) into f(x), resulting in f(g(x)) = sqrt(x + 4).

In more detail, a composite function is created when one function is applied to the result of another function. Here, we have two functions: \( f(x) = \sqrt{x} \) and \( g(x) = x + 4 \). To form the composite function \( (f \circ g)(x) \), we need to substitute the output of \( g(x) \) into \( f(x) \).

First, let's find \( g(x) \). For any input \( x \), \( g(x) \) adds 4 to \( x \). So, \( g(x) = x + 4 \).

Next, we take this result and use it as the input for \( f(x) \). The function \( f(x) \) takes the square root of its input. Therefore, we replace the \( x \) in \( f(x) = \sqrt{x} \) with \( g(x) \), which is \( x + 4 \).

So, \( f(g(x)) = f(x + 4) = \sqrt{x + 4} \).

Thus, the composite function \( (f \circ g)(x) \) is \( \sqrt{x + 4} \). This means that for any value of \( x \), you first add 4 to \( x \) and then take the square root of the result.