Question

find the range of f(x) = 1-|x-2|

Answer 1

Answer:

The range of the function is $R=(-\infty,1],\{y|y\leq 1\}$

Step-by-step explanation:

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

To find : The range of the expression ?

Solution :

The range is defined as the set of all valid  y  values.

or The range is the set of values that correspond with the domain.

If we the first find the domain of the function i.e. the set of values where function is defined.

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

The domain of the function is $D=(-\infty,\infty),\{x|x\in\mathbb{R}\}$

When $x\rightarrow -\infty$

Then y approaches to $-\infty$

When $x\rightarrow \infty$

Then y approaches to 1.

So, The range of the function is $R=(-\infty,1],\{y|y\leq 1\}$