91Ó°ÊÓ

Function substitution is a process where we replace the variable, often represented as x, with a specific value. This helps us find the output of the function for that particular value. In the provided example, we have the function \(f(x) = x^{1/2}\). To evaluate \(f(4)\), we substitute 4 in place of x:

• Identify the variable in the function (here it's x)
• Replace x with the given value (4 in this case)

By doing this, we essentially change the expression inside the function and then move on to solve it.

The square root function is a type of exponential function where the exponent is 1/2. When evaluating the square root, you're looking for a number that, when multiplied by itself, gives you the original number. The notation for the square root of a number a is \( \sqrt{a} \).

For example:

• \( \sqrt{4} = 2 \,\,\text{because} \,\, 2 \cdot 2 = 4 \)
• \( \sqrt{9} = 3 \,\,\text{because} \,\, 3 \cdot 3 = 9 \)

Finding the square root is common in many different problems and is a fundamental concept in algebra. In our exercise, we applied the square root function to the value 4, which simplified to 2, as \(2 \cdot 2 = 4\).

Function evaluation means calculating the value of a function for a particular input. This includes the steps of substitution and any necessary mathematical operations. For the function \( f(x) = x^{1/2} \), evaluating \( f(4) \) involves:

• Substituting the value into the function, turning it into \(f(4) = 4^{1/2} \)
• Calculating the square root of 4 (which is 2)

The final result we obtain from this process is the value of the function at that specific point. In this case, \(f(4) = 2\).

This systematic approach helps ensure that we follow the correct steps to find the output. Understanding this concept is crucial when tackling various mathematical functions. By practicing function evaluation, you'll become more comfortable with different types of functions, like linear, quadratic, and more complex ones.