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∘g)(x) means to apply g first and then apply f to the result. In this case, (ƒ∘ƒ)(2) means to first find ƒ(2) and then use that result as the input for ƒ again.
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Evaluating Functions
Evaluating a function means substituting a specific value into the function's formula to find the output. For example, to evaluate ƒ(x) = 2x - 3 at x = 2, you would calculate ƒ(2) = 2(2) - 3, which simplifies to 1. This process is essential for finding function values in composition.
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Evaluating Composed Functions
Linear Functions
Linear functions are mathematical expressions that create a straight line when graphed. They can be represented in the form ƒ(x) = mx + b, where m is the slope and b is the y-intercept. Both ƒ(x) = 2x - 3 and g(x) = -x + 3 are linear functions, which means their compositions will also yield linear results.
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