Question

If $x = -0.5$, then which of the following has the smallest value?

• A. $\frac{1}{2^x}$
• B. $\frac{1}{x}$
• C. $\frac{1}{x^2}$
• D. $2^x$
• E. $\frac{1}{\sqrt{-x}}$

Hint:

Check signs first when comparing values; negative numbers are always smaller than positive ones.

Answer 1

The Correct Option is D

For $x = -0.5$: \[ 2^x = 2^{-0.5} = \frac{1}{\sqrt{2}} \approx 0.707 \] \[ \frac{1}{2^x} = 2^{0.5} \approx 1.414 \] \[ \frac{1}{x} = \frac{1}{-0.5} = -2 \] \[ \frac{1}{x^2} = \frac{1}{0.25} = 4 \] \[ \frac{1}{\sqrt{-x}} = \frac{1}{\sqrt{0.5}} \approx 1.414 \] Clearly, the smallest is -2, which corresponds to $\frac{1}{x}$. \[ \boxed{\frac{1}{x}} \]