Find the domain and the range of each of the following real function:

Given: $f(x)=1-|x-2|$

Need to find: Where the functions are defined.

Since $|x-2|$ gives real no. for all values of $x$, the domain set can possess any real numbers.

So, the domain of the function, $\operatorname{Df}(x)=(-\infty, \infty)$.

Now the given function is $f(x)=1-|x-2|$, where $|x-2|$ is always positive. So, the maximum value of the function is 1 .

Therefore, the range of the function, $\mathrm{R} \mathrm{f}(\mathrm{x})=(-\infty, 1)$