If [tex]f(x)=2 x^2+1[/tex], what is [tex]f(x)[/tex] when [tex]x=3[/tex]?

Substitute x = 3 into the function f ( x ) = 2 x 2 + 1 .
Calculate 3 2 = 9 .
Multiply the result by 2: 2 × 9 = 18 .
Add 1 to get the final answer: 18 + 1 = 19 . The final answer is 19 ​ .

Explanation

Understanding the problem We are given the function f ( x ) = 2 x 2 + 1 and we want to find the value of f ( x ) when x = 3 . This means we need to substitute x = 3 into the expression for f ( x ) .

Substitution Now, let's substitute x = 3 into the function: f ( 3 ) = 2 ( 3 ) 2 + 1

Calculation Next, we need to calculate the value of f ( 3 ) . First, we calculate 3 2 which is 3 × 3 = 9 . Then, we multiply this result by 2, which gives us 2 × 9 = 18 . Finally, we add 1 to this result: 18 + 1 = 19 .
f ( 3 ) = 2 ( 9 ) + 1 = 18 + 1 = 19

Final Answer Therefore, the value of f ( x ) when x = 3 is 19.


Examples
Imagine you are designing a bridge and need to calculate the load at a specific point. The function f ( x ) = 2 x 2 + 1 could represent the stress on the bridge at a distance x from the center. By finding f ( 3 ) , you determine the stress at 3 meters from the center, ensuring the bridge's structural integrity. This type of calculation is crucial in engineering to predict and manage stress distribution in structures.

Answered by GinnyAnswer | 2025-07-03

By substituting x = 3 into the function f ( x ) = 2 x 2 + 1 , we calculated that f ( 3 ) = 19 through a series of steps: squaring, multiplying, and adding. The final result is 19 .
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Answered by Anonymous | 2025-07-04