Evaluate 3f(2) = . what does this equal
The correct answer and explanation is:
To evaluate 3f(2), we must understand the expression. This notation involves a function and scalar multiplication. Here’s how to interpret and solve it.
Correct Answer:
3f(2) means 3 multiplied by the value of the function f when x = 2, or: 3f(2)=3×f(2)3f(2) = 3 \times f(2)
However, to evaluate this expression, we need to know what the function f(x) is. Without a definition for f(x) (e.g., f(x)=2x+1f(x) = 2x + 1 or any other rule), we cannot calculate a specific number.
If, for example, the function is given as: f(x)=2x+1f(x) = 2x + 1
then: f(2)=2(2)+1=4+1=5f(2) = 2(2) + 1 = 4 + 1 = 5
and: 3f(2)=3×5=153f(2) = 3 \times 5 = 15
But if no definition of f(x) is provided, then 3f(2) remains an unevaluated expression. So, the final answer depends on the value of f(2).
300-Word Explanation:
In mathematics, when you see an expression like 3f(2), it’s shorthand for scalar multiplication involving a function. The “f” represents a function, which is a rule that assigns each input xx to exactly one output f(x)f(x).
The notation f(2) specifically asks, “What is the value of the function f when the input is 2?” After finding that value, you then multiply it by 3.
To solve this, you need to know the function’s rule—something like:
- f(x)=x+4f(x) = x + 4
- f(x)=3×2−1f(x) = 3x^2 – 1
- Or any other formula.
For instance, if f(x)=x2f(x) = x^2, then: f(2)=22=4,so3f(2)=3×4=12.f(2) = 2^2 = 4,\quad \text{so} \quad 3f(2) = 3 \times 4 = 12.
This process is a two-step operation:
- Plug the input value (2) into the function to find f(2)f(2).
- Multiply the result by 3.
Without knowing what f(x) is, the value of f(2) is unknown. That makes 3f(2) undefined in numeric terms until we get that information.
Therefore, you must be given a definition of the function f(x) in order to evaluate 3f(2). If it’s not provided, you can only simplify it as 3 × f(2) and not compute a numerical answer.