Evaluate the function. Find [tex]$f(2)$[/tex] when [tex]$f(x) = x^2 + 4x + 3$[/tex].
Answer (2)
Substitute x = 2 into the function f ( x ) = x 2 + 4 x + 3 .
Calculate f ( 2 ) = ( 2 ) 2 + 4 ( 2 ) + 3 .
Simplify the expression: f ( 2 ) = 4 + 8 + 3 = 15 .
The final answer is 15 .
Explanation
Understanding the problem We are given the function f ( x ) = x 2 + 4 x + 3 and asked to find the value of f ( 2 ) . This means we need to substitute x = 2 into the expression for f ( x ) and simplify.
Substitution Substitute x = 2 into the function: f ( 2 ) = ( 2 ) 2 + 4 ( 2 ) + 3
Simplification Now, we simplify the expression: f ( 2 ) = 4 + 8 + 3 f ( 2 ) = 12 + 3 f ( 2 ) = 15
Final Answer Therefore, the value of the function f ( x ) at x = 2 is 15.
Examples
Evaluating functions is a fundamental concept in mathematics and has numerous real-world applications. For example, if you're tracking the trajectory of a ball thrown in the air, the function might describe the height of the ball at a given time x . Evaluating the function at a specific time, like x = 2 seconds, tells you the height of the ball at that moment. Similarly, in business, a cost function might describe the total cost of producing x items. Evaluating the cost function at a specific quantity, like x = 200 items, tells you the total cost of producing that many items. These examples show how evaluating functions helps us understand and predict outcomes in various situations.
To find f ( 2 ) for the function f ( x ) = x 2 + 4 x + 3 , substitute x with 2 to get f ( 2 ) = 15 . This involves calculating each term separately and summing them up. Thus, the final answer is 15 .
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