Question

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

Answer 1

Answer:

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

Step-by-step explanation:

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

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

When xarrow -\inftyxarrow−∞

Then y approaches to -\infty−∞

When xarrow \inftyxarrow∞

Then y approaches to 1.

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