Proving the Statement: 'f(x) = x^2' for All Real Numbers

Is the statement 'f(x) = x^2' True for all real numbers?

Let's evaluate the function f(x) = x^2 for different values of x to determine the truth of this statement. Is it True or False?

Answer:

The statement 'f(x) = x^2' is True for all real numbers.

When evaluating the function f(x) = x^2 for various real numbers, we find that the output matches the input squared for all cases. This confirms that the statement is indeed True for all real numbers.

To illustrate this, consider substituting x = 2 into the function. We get f(2) = 2^2 = 4, which is equal to 2 squared. Similarly, substituting x = -3 gives us f(-3) = (-3)^2 = 9, where 9 is equal to (-3) squared.

By examining these examples and applying the same logic to any other real number for x, we consistently find the output to be equal to the input squared. This comprehensive analysis validates the statement that 'f(x) = x^2' is indeed True for all real numbers.

For further understanding on evaluating a function, you can explore more resources or seek additional explanations. Remember, mathematical statements like these are crucial in building a strong foundation in algebraic concepts.