An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
First, find the value of f ( − 5 ) from the table: f ( − 5 ) = 3 .
Next, find the value of g ( f ( − 5 )) = g ( 3 ) from the table: g ( 3 ) = 1 .
Therefore, ( g c i rc f ) ( − 5 ) = 1 .
The final answer is 1 .
Explanation
Understanding the composite function We need to evaluate the composite function ( g c i rc f ) ( − 5 ) . This means we first evaluate f ( − 5 ) and then use that result as the input for the function g .
Evaluating f(-5) From the table for f ( x ) , we find that when x = − 5 , f ( − 5 ) = 3 .
Evaluating g(3) Now we need to find g ( f ( − 5 )) , which is g ( 3 ) . From the table for g ( x ) , we find that when x = 3 , g ( 3 ) = 1 .
Final result Therefore, ( g c i rc f ) ( − 5 ) = g ( f ( − 5 )) = g ( 3 ) = 1 .
Examples
Composite functions are used in many real-world applications. For example, in manufacturing, a composite function can describe the cost of producing a certain number of items, where one function gives the number of items produced as a function of time, and another function gives the cost as a function of the number of items produced. Combining these functions gives the cost as a function of time. Another example is in computer graphics, where composite functions are used to apply multiple transformations to an object, such as rotating and scaling it.
The total charge delivered by a 15.0 A current for 30 seconds is 450 C . Dividing this by the charge of an electron shows that approximately 2.81 × 1 0 21 electrons flow through the device. This demonstrates the relationship between current, charge, and the number of electrons.
;
