Final answer:
To create a composite function from f(x) and g(x), one function is substituted into the other. For example, f(g(x)) is found by replacing x in f(x) with g(x). The resulting expression is then simplified or evaluated at specific values of x.
Step-by-step explanation:
The student's question involves creating and evaluating a composite function using the functions f(x) = x^2 + 3x - 5 and g(x) = 2x^2 - 4x + 6. To set up the composite function, we choose one function to substitute into the other. For instance, the composite function f(g(x)) involves replacing every x in f(x) with g(x), which gives us:
f(g(x)) = (2x^2 - 4x + 6)^2 + 3(2x^2 - 4x + 6) - 5.
We then expand and simplify this expression to evaluate the composite function at specific values of x, or to study the properties of the resulting function. If the student provided a specific value for x, we would proceed to plug that value into the composite function and simplify to obtain the result. Keep in mind that the composite function's domain is defined by where both f(x) and g(x) are defined.