Question
2.2 For which values of \( x \) is the expression \( \sqrt{1-2 x} \) non real?
Ask by Rowe Lynch. in South Africa
Mar 17,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The expression \(\sqrt{1-2x}\) is non-real when \(x > \frac{1}{2}\).
Solution
1. We need the expression \(\sqrt{1-2x}\) to be non-real. The square root function is non-real when its radicand is negative.
2. Set up the inequality for the radicand to be negative:
\[
1 - 2x < 0.
\]
3. Solve the inequality:
- Subtract 1 from both sides:
\[
-2x < -1.
\]
- Divide both sides by \(-2\) and remember to reverse the inequality sign:
\[
x > \frac{1}{2}.
\]
4. Therefore, the expression \(\sqrt{1-2x}\) is non-real when:
\[
x > \frac{1}{2}.
\]
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Simplify this solution Bonus Knowledge
The expression \( \sqrt{1-2x} \) is non-real when the value inside the square root is negative. This occurs when \( 1 - 2x < 0 \). Solving this inequality gives us \( 1 < 2x \) or \( \frac{1}{2} < x \). Therefore, \( \sqrt{1-2x} \) is non-real for all values of \( x \) greater than \( \frac{1}{2} \). In simpler terms, if you pick any number greater than \( 0.5 \) for \( x \), you'll end up with a square root of a negative number, and that’s when things get imaginary! So, keep your choices below or equal to \( 0.5 \) to stay in the realm of real numbers.
