What is value of a function f(x)f(x)f(x) at x=5x = 5x=5?
The correct Answer and Explanation is:
To determine the value of a function ( f(x) ) at ( x = 5 ), we need to know the specific form of the function ( f(x) ). The function could be linear, quadratic, or any other type, and the form of ( f(x) ) will dictate how we calculate its value at ( x = 5 ).
Let’s assume a few different scenarios to explain how to solve this problem:
Example 1: Linear Function
If the function is linear, say ( f(x) = 2x + 3 ), we can find ( f(5) ) by substituting ( x = 5 ) into the equation.
[
f(5) = 2(5) + 3 = 10 + 3 = 13
]
So, the value of ( f(x) ) at ( x = 5 ) is 13 for this specific function.
Example 2: Quadratic Function
If the function is quadratic, say ( f(x) = x^2 – 4x + 6 ), then to find ( f(5) ), we again substitute ( x = 5 ) into the equation:
[
f(5) = (5)^2 – 4(5) + 6 = 25 – 20 + 6 = 11
]
Here, the value of ( f(x) ) at ( x = 5 ) is 11 for this quadratic function.
Example 3: Polynomial Function
Let’s consider a more complex polynomial function, such as ( f(x) = 3x^3 – 2x^2 + x – 1 ). To find ( f(5) ), we substitute ( x = 5 ):
[
f(5) = 3(5)^3 – 2(5)^2 + 5 – 1 = 3(125) – 2(25) + 5 – 1 = 375 – 50 + 5 – 1 = 329
]
In this case, the value of ( f(x) ) at ( x = 5 ) is 329.
Conclusion
To find the value of a function at a specific point like ( x = 5 ), you need to know the exact form of the function. Once you have that, solving for ( f(5) ) is just a matter of substituting ( x = 5 ) into the function’s equation and performing basic arithmetic operations. Each type of function (linear, quadratic, polynomial) will result in a different value at ( x = 5 ).