Mathematics - Functions Question with Solution | TestHub

$f\left(x\right)=\frac{2e^{2x}}{e^{2x}+e}$

$f\left(1-x\right)=\frac{2e^{2\left(1-x\right)}}{e^{2\left(1-x\right)}+e}=\frac{2e}{e+e^{2x}}$

Now, $f\left(x\right)+f\left(1-x\right)=2$ 

i.e. $f\left(\frac{1}{100}\right)+f\left(\frac{99}{100}\right)=2$

$\Rightarrow f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+\mathrm{...}f\left(\frac{99}{100}\right)=2\times 49+f\left(\frac{50}{100}\right)$

$=98+1=99$