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ANSWER
all real numbers
EXPLANATION
The given absolute value function is
This function is obtained by shifting the graph of
to the left by 2 units.
Since the domain of the parent function is all real numbers, the domain of the transformed function is also all real numbers because the shifting the parent function horizontally or vertically does not affect the domain.
We can check the equation is an extraneous solution or not by finding the solution and plugging it in the equation, to verify it.
<h3>What is the extraneous solution?</h3>In mathematics, an extraneous solution is a solution that comes from the process of solving the problem but is not a genuine solution to the problem, such as the answer to an equation.
As we know from the definition the extraneous solution is a solution that comes from the process of solving the problem but is not a genuine solution to the problem.
Let's suppose the equation is:
Squaring both the sides:
x + 4 = (x - 2)²
x + 4 = x² - 4x + 4
x² -5x = 0
x = 0 or x = 5
Checking for the solution by plugging in the equation;
3 = 3
2 ≠ -2
The solution x = 0 shows extraneous solution.
Thus, we can check the equation is an extraneous solution or not by finding the solution and plugging it in the equation, to verify it.
Learn more about the extraneous solution here:
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