For which values of x is the expression undefined?

Understand the Problem

The question is asking for the specific values of x that make the given expression undefined. This usually occurs when there is a division by zero or when taking the square root of a negative number in the context of real numbers. To solve this, we would need to identify any restrictions based on the expression provided.

Answer

The specific values of $x$ that make the expression undefined depend on the structure of the given expression.

Steps to Solve

Identify the expression for undefined values

First, look closely at the expression that leads to undefined situations. Typically, this involves fractions where the denominator becomes zero or square roots where the radicand is negative.

Set the denominator to zero

If the expression has a denominator of the form $f(x)$, set it to zero and solve for $x$: $$ f(x) = 0 $$

Solve for x

After determining the function, solve the equation from the previous step for $x$. This will give you the values that make the expression undefined.

Check for square roots (if applicable)

If your expression includes a square root, set the radicand to be zero or greater, solving: $$ g(x) \geq 0 $$ This ensures that you are only considering values of $x$ that do not lead to a square root of a negative number.

Summarize undefined values

Collect all the values of $x$ found in the previous steps, as these are the specific values that make the expression undefined.

The final answer will depend on the specific expression you have.

More Information

When working with expressions, it’s essential to remember that undefined values are critical in determining the domain of a function. The concept is widely applicable in algebra and calculus.

Tips

Not checking both the denominator and any square roots, which can lead to missing some undefined values.
Forgetting that equalities can also be strict; for example, $g(x) = 0$ is often included in the points to check.

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