The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is
$(0, 1]$
$[0, 1]$
$( - \infty ,\;0]$
$( - \infty ,\;1)$
Let ${f_k}\left( x \right) = \frac{1}{k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)\;,x \in R$ and $k \ge 1$, then ${f_4}\left( x \right) - {f_6}\left( x \right)$ is equal to
If $f(x) = \frac{{{x^2} - 1}}{{{x^2} + 1}}$, for every real numbers. then the minimum value of $f$
Domain of the function $f(x) =$ $\frac{1}{{\sqrt {\ln \,{{\cot }^{ - 1}}x} }}$ is
Consider a function $f : N \rightarrow R$, satisfying $f(1)+2 f(2)+3 f(3)+\ldots+x f(x)=x(x+1) f(x) ; x \geq 2$ with $f(1)=1$. Then $\frac{1}{f(2022)}+\frac{1}{f(2028)}$ is equal to