Here are the essential concepts you must grasp in order to answer the question correctly.
Function Composition
Function composition involves combining two functions to create a new function. The notation (ƒg)(x) means to apply g first and then apply f to the result. This is calculated as ƒ(g(x)), where you substitute g(x) into the function f. Understanding this concept is crucial for solving problems that require evaluating the composition of functions.
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Evaluating Functions
Evaluating functions means finding the output of a function for a given input. For example, to evaluate g(-3), you substitute -3 into the function g(x) = -2x + 6. This process is essential for function composition, as you first need to evaluate the inner function before applying the outer function.
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Quadratic Functions
A quadratic function is a polynomial function of degree two, typically expressed in the form f(x) = ax^2 + bx + c. In this case, f(x) = x^2 + 3 is a quadratic function where a = 1, b = 0, and c = 3. Understanding the properties of quadratic functions, such as their shape (parabola) and vertex, is important when evaluating them in the context of function composition.
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