The domain and range of real function $f$ defined by $f(x)=\sqrt{x-1}$ is given by
The domain of the function $f$ given by $f(x)=\frac{x^2+2 x+1}{x^2-x-6}$.
The domain and range of the function $f$ given by $f(x)=2-|x-5|$ is
The domain for which the functions defined by $f(x)=3 x^2-1$ and $g(x)=3+x$ are equal to
Let $f$ and $g$ be two real functions given by
$$\text { and } \quad \begin{aligned} f & =\{(0,1),(2,0),(3,-4),(4,2),(5,1)\} \\ & =\{(1,0),(2,2),(3,-1),(4,4),(5,3)\} \end{aligned}$$
then the domain of $f \cdot g$ is given by........... .
$$\begin{aligned} \text{We have,}\quad f & =\{(0,1),(2,0),(3,-4),(4,2),(5,1)\} \\ \text{and}\quad g & =\{(1,0),(2,2),(3,-1),(4,4),(5,3)\} \end{aligned}$$
$\begin{array}{ll}\therefore & \text { Domain of } f=\{0,2,3,4,5\}, \\ \text { and } & \text { Domain of } g=\{1,2,3,4,5\}\end{array}$
$$\therefore$$ Domain of $(f . g)=$ Domain of $f~\cap$ Domain of $g=\{2,3,4,5\}$