The equation of function \(f\) is given below.
\[f(x)=2 x^2+x+1\]
What is the value of \(f(-3)\)?
Answer (2)
Substitute x = − 3 into the function f ( x ) = 2 x 2 + x + 1 .
Calculate f ( − 3 ) = 2 ( − 3 ) 2 + ( − 3 ) + 1 .
Simplify the expression: f ( − 3 ) = 18 − 3 + 1 = 16 .
The value of the function at x = − 3 is 16 .
Explanation
Understanding the problem We are given the function f ( x ) = 2 x 2 + x + 1 and we want to find the value of f ( − 3 ) . This means we need to substitute − 3 for x in the expression for f ( x ) .
Substituting x = -3 Now, let's substitute x = − 3 into the function: f ( − 3 ) = 2 ( − 3 ) 2 + ( − 3 ) + 1
Simplifying the expression Next, we simplify the expression: f ( − 3 ) = 2 ( 9 ) − 3 + 1 f ( − 3 ) = 18 − 3 + 1 f ( − 3 ) = 15 + 1 f ( − 3 ) = 16
Final Answer Therefore, the value of f ( − 3 ) is 16.
Examples
Understanding functions and evaluating them at specific points is crucial in many real-world applications. For example, in physics, the height of a projectile might be modeled by a quadratic function. Evaluating the function at a specific time tells you the height of the projectile at that time. Similarly, in economics, a cost function might describe the cost of producing a certain number of items. Evaluating the cost function tells you the cost for a specific production level. This concept is also used in computer science for algorithm analysis, where functions describe the performance of an algorithm, and evaluating them helps predict the algorithm's behavior for different input sizes.
By substituting − 3 into the function f ( x ) = 2 x 2 + x + 1 , we find that f ( − 3 ) equals 16. The steps include calculating powers and performing arithmetic operations. Therefore, the final result is f ( − 3 ) = 16 .
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