Mathematics - Functions Question with Solution | TestHub

$\begin{array}{rl}& f(x)=\frac{42^x+16}{2.2^{2x}+16.2^x+32}\\ & f(x)=\frac{2\left(2^x+4\right)}{2^{2x}+8.2^x+16}\\ & f(x)=\frac{2}{2^x+4}\\ & f(4-x)=\frac{2^x}{2\left(2^x+4\right)}\\ & f(x)+f(4-x)=\frac{1}{2}\end{array}$

So, $\mathrm{f}\left(\frac{1}{15}\right)+\mathrm{f}\left(\frac{59}{15}\right)=\frac{1}{2}$
$\begin{array}{rl}& \text{ Similarly }=f\left(\frac{29}{15}\right)+f\left(\frac{31}{15}\right)=\frac{1}{2}\\ & f\left(\frac{30}{15}\right)=f(2)=\frac{2}{2^2+4}=\frac{2}{8}=\frac{1}{4}\\ & \Rightarrow 8\left(29\times \frac{1}{2}+\frac{1}{4}\right)\end{array}$

Ans. 118