Complete the range of the function
f(x)=sqrt(x^2). Thank you!
To find the range of the function f(x) = √(x^2), we need to determine all possible output values or y-values that the function can produce.
First, let's analyze the function √(x^2). In this case, the square root operation ensures that the output is always positive or zero, regardless of the input value. Therefore, the range of the function f(x) is all non-negative real numbers, or [0, ∞).
To understand how we arrived at this conclusion, we can break down the steps:
Step 1: Identify the function: f(x) = √(x^2)
Step 2: Consider the domain of x: Since x can take any real number, there are no restrictions on the input values.
Step 3: Evaluate the function for various input values: By trying out different values of x, we observe that f(x) = √(x^2) always produces non-negative values.
Step 4: Determine the range: Since the function only outputs non-negative values, the range of f(x) is [0, ∞).
Therefore, the range of the function f(x) = √(x^2) is [0, ∞).