Question

Find the domain and range of the real function f defined by $f\left(x\right)=\sqrt{x-1}$.

Answer 1

Here $f\left(x\right)=\sqrt{x-1},f\left(x\right)$ assumes real values if $x-1\ge 0\Rightarrow x\ge 1\Rightarrow xϵ[1,\infty )$

$\therefore$ Domain of $f\left(x\right)=[1,\infty )$

For $x\ge 1,f\left(x\right)\ge 0$

$\therefore$ Range of f(x) = all real numbers $\ge 0$

$=[0,\infty )$