Here are the essential concepts you must grasp in order to answer the question correctly.
Function Evaluation
Function evaluation involves substituting a specific input value into a function to determine its output. For example, if f(x) is a function, finding f(2) means determining the value of f when x equals 2. This concept is fundamental in understanding how functions behave at specific points.
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Product of Functions
The product of two functions, denoted as (fg)(x), is defined as the multiplication of their outputs at a given input x. Specifically, (fg)(x) = f(x) * g(x). To find (fg)(2), one must first evaluate f(2) and g(2), then multiply these results together, illustrating how functions can interact through multiplication.
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Graph Interpretation
Interpreting graphs of functions involves analyzing visual representations to extract information about the functions' values at specific points. In this case, the graphs of f(x) and g(x) can be used to find f(2) and g(2) by locating the corresponding y-values at x = 2. This skill is crucial for solving problems that require understanding the behavior of functions graphically.
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