Answer :
- Substitute $x = 5$ into the function $f(x) = 3x^2 + 2x - 1$.
- Calculate $f(5) = 3(5)^2 + 2(5) - 1$.
- Simplify the expression: $f(5) = 75 + 10 - 1 = 84$.
- The value of the function at $x=5$ is $\boxed{84}$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = 3x^2 + 2x - 1$ and asked to find the value of $f(5)$. This means we need to substitute $x = 5$ into the expression for $f(x)$ and simplify.
2. Substitution
Substitute $x = 5$ into the function:$$f(5) = 3(5)^2 + 2(5) - 1$$
3. Simplifying the expression
Now, we simplify the expression using the order of operations. First, we calculate $5^2 = 25$. Then, we have:$$f(5) = 3(25) + 2(5) - 1$$Next, we perform the multiplications:$$f(5) = 75 + 10 - 1$$Finally, we add and subtract:$$f(5) = 85 - 1 = 84$$
4. Final Answer
Therefore, the value of $f(5)$ is 84.
### Examples
Understanding how to evaluate functions is crucial in many real-world applications. For example, if you're modeling the trajectory of a ball thrown in the air, the function might describe the height of the ball at different times. Evaluating the function at a specific time tells you the height of the ball at that moment. Similarly, in economics, a cost function might describe the cost of producing a certain number of items. Evaluating the function tells you the cost for a specific production level.
- Calculate $f(5) = 3(5)^2 + 2(5) - 1$.
- Simplify the expression: $f(5) = 75 + 10 - 1 = 84$.
- The value of the function at $x=5$ is $\boxed{84}$.
### Explanation
1. Understanding the problem
We are given the function $f(x) = 3x^2 + 2x - 1$ and asked to find the value of $f(5)$. This means we need to substitute $x = 5$ into the expression for $f(x)$ and simplify.
2. Substitution
Substitute $x = 5$ into the function:$$f(5) = 3(5)^2 + 2(5) - 1$$
3. Simplifying the expression
Now, we simplify the expression using the order of operations. First, we calculate $5^2 = 25$. Then, we have:$$f(5) = 3(25) + 2(5) - 1$$Next, we perform the multiplications:$$f(5) = 75 + 10 - 1$$Finally, we add and subtract:$$f(5) = 85 - 1 = 84$$
4. Final Answer
Therefore, the value of $f(5)$ is 84.
### Examples
Understanding how to evaluate functions is crucial in many real-world applications. For example, if you're modeling the trajectory of a ball thrown in the air, the function might describe the height of the ball at different times. Evaluating the function at a specific time tells you the height of the ball at that moment. Similarly, in economics, a cost function might describe the cost of producing a certain number of items. Evaluating the function tells you the cost for a specific production level.
