Question

If $ f\left(x\right) = \frac{4^{x}}{4^{x}+2} $ , then $ f\left(\frac{1}{97}\right)+f\left(\frac{2}{97}\right)+\ldots+ f\left(\frac{96}{97}\right) $ is equal to

• A. 1
• B. 48
• C. -48
• D. -1

Answer 1

Answer: (B)

For $\frac{1}{97} \leq x \leq \frac{96}{97}$,
$1<4^{x}<4$
$\Rightarrow \frac{1}{3}<\frac{4^{x}}{4^{x}+2}<\frac{4}{6}$
$\Rightarrow 0.33<\frac{4^{x}}{4^{x}+2}<0.66$
$\Rightarrow 0.33 \times 96<\frac{4^{x}}{4^{x}+2} \times 96<0.66 \times 96$
$=31.68<\frac{4^{x}}{4^{x}+2} \times 96<63.36$