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 (ƒ o g)(x) means to apply g first and then apply f to the result of g. This is essential for solving the problem, as it requires evaluating f at the output of g, which is a fundamental operation in algebra.
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Solving Equations
Solving equations is the process of finding the values of variables that satisfy a given mathematical statement. In this context, we need to set the composed function (ƒ o g)(x) equal to 7 and solve for x. This involves manipulating the equation to isolate x, which is a critical skill in algebra.
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Quadratic Functions
Quadratic functions are polynomial functions of degree two, typically expressed in the form g(x) = ax² + bx + c. In this problem, g(x) is a quadratic function, and understanding its properties, such as its vertex and roots, is important for analyzing the output of g and how it interacts with f in the composition.
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