The domain of the function $f(x) = {\sin ^{ - 1}}[{\log _2}(x/2)]$ is
$[1, 4]$
$[-4, 1]$
$[-1, 4]$
None of these
Let $R$ be the set of all real numbers and let $f$ be a function from $R$ to $R$ such that $f(x)+\left(x+\frac{1}{2}\right) f(1-x)=1$, for all $x \in R$. Then $2 f(0)+3 f(1)$ is equal to
Consider the identity function $I _{ N }: N \rightarrow N$ defined as $I _{ N }$ $(x)=x$ $\forall $ $x \in N$ Show that although $I _{ N }$ is onto but $I _{ N }+ I _{ N }:$ $ N \rightarrow N$ defined as $\left(I_{N}+I_{N}\right)(x)=$ $I_{N}(x)+I_{N}(x)$ $=x+x=2 x$ is not onto.
Show that the function $f: N \rightarrow N$ given by $f(x)=2 x,$ is one-one but not onto.
The domain of the definition of the function $f\left( x \right) = \frac{1}{{4 - {x^2}}} + \log \,\left( {{x^3} - x} \right)$ is
Range of the function $f(x) = {\sin ^2}({x^4}) + {\cos ^2}({x^4})$ is