Question

The range of the function $f(x)=\left(\frac{1}{3}\right)^{3+\sin x}$ is

• A. $\left[-\frac{1}{9},\frac{1}{81}\right]$
• B. $\left[-\frac{1}{9},\frac{1}{3}\right]$
• C. $\left[\frac{1}{9},\frac{1}{3}\right]$
• D. $\left[\frac{1}{81},\frac{1}{9}\right]$
• E. $\left[\frac{1}{81},\frac{1}{3}\right]$

Hint:

Logic Tip: Always pay attention to the base of an exponential function. If the base $b>1$, the function preserves inequality directions. If $0<b<1$ (like 1/3 here), the function reverses the inequality directions.

Answer 1

The Correct Option is D