If $f:R\to R$ be defined as follows: $f\left(x\right)=\{\begin{array}{c}1,ifx\in Q\\ -1,ifx\notin Q\end{array}$. Find $f\left(\frac{1}{2}\right)$,range of f
and pre-images of $1$ and $-1$

If $f:R\to R$ is defined by
$f\left(x\right)=\{\begin{array}{ccc}\frac{x+2}{x^2+3x+2},& if& x\in R-\{-1,-2\}\\ -1,& if& x=-2\\ 0,& if& x=-1\end{array}$
then $f$ is continuous on the set

IF f:R to R be defined as follows:
F(x)= {1, if x belongs to Q}
F(x)={-1,if x does not belongs to Q}
find
1)f(1/2),f(pi), f(root 2)
2)range of f
3)pre images of 1 and -1

Let $f:R\to R$ be defined by
$f\left(x\right)=\{\begin{array}{c}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}$
If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is

Let $f:R\to R$ be defined by $f\left(x\right)=\{\begin{array}{c}k-2x,ifx\le -1\\ 2x+3,ifx>-1\end{array}$ be continous. then find possible value of $k$ is

If $0<a<1$ and $f$ is defined as $f\left(x\right)=\{\begin{array}{c}{x}^a;ifx>0\\ 0;ifx=0\end{array}$