If [tex]f(x)=5+4 x^2[/tex], then [tex]f(3)=[/tex]?
Answer (1)
Substitute x = 3 into the function f ( x ) = 5 + 4 x 2 .
Calculate 3 2 = 9 .
Multiply the result by 4: 4 × 9 = 36 .
Add 5 to the result: 5 + 36 = 41 . The final answer is 41 .
Explanation
Understanding the problem We are given the function f ( x ) = 5 + 4 x 2 and we need to find the value of f ( 3 ) . This means we need to substitute x = 3 into the expression for f ( x ) .
Substitution Substitute x = 3 into the function: f ( 3 ) = 5 + 4 ( 3 ) 2
Calculation Now, we simplify the expression. First, we calculate 3 2 = 3 × 3 = 9 . Then, we multiply this result by 4: 4 × 9 = 36 . Finally, we add 5 to this result: 5 + 36 = 41 . Therefore, f ( 3 ) = 5 + 4 ( 9 ) = 5 + 36 = 41
Final Answer Thus, the value of the function f ( x ) when x = 3 is 41.
Examples
In physics, the function f ( x ) = 5 + 4 x 2 could represent the potential energy of an object, where x is the position of the object. Evaluating f ( 3 ) would then give the potential energy of the object at position x = 3 . This kind of calculation is crucial in understanding the behavior of physical systems and predicting their future states. Understanding function notation and evaluation is therefore essential for modeling and analyzing real-world phenomena.
