Here are the essential concepts you must grasp in order to answer the question correctly.
Function Notation
Function notation, such as f(x), represents a mathematical relationship where 'f' is the function name and 'x' is the input variable. The output of the function is determined by substituting the input value into the function's rule. Understanding function notation is essential for evaluating functions at specific values.
Recommended video:
Greatest Integer Function
The greatest integer function, denoted as [[x]], returns the largest integer less than or equal to x. For example, [[3.7]] equals 3, as it rounds down to the nearest whole number. This concept is crucial for solving the given function, as it directly affects the output when evaluating f(x).
Recommended video:
Intro to Rational Functions
Evaluating Functions
Evaluating a function involves substituting a specific value for the variable and calculating the result based on the function's definition. In this case, to find f(3.7), one must first compute [[-3.7]], then apply the function's formula. Mastery of this process is vital for accurately determining function values.
Recommended video:
Evaluating Composed Functions