Question

The domain of the function $f\left(x\right)=\sum _{n=1}^{10}\frac{1}{\left|2x-n\right|}$ is __________ .

Answer 1

f(x) = $\sum _{n=1}^{10}\frac{1}{\left|2x-n\right|}$

f(x) is not defined if 2x − n = 0

$\mathrm{i}.\mathrm{e}x=\frac{n}{2};n=1\mathrm{to}10$
∴ Domain of f(x) is $\mathrm{ℝ}~\left\{\frac{1}{2},1,\frac{3}{2},2,\frac{5}{2},3,\frac{7}{2},4,\frac{9}{2},5\right\}$