Question

Find the domain and range of the functions f(x) = 1 - |x − 2|
Pls answer fast

Answer 1

$\large\underline{\sf{Solution-}}$

Given function is

$\rm :\longmapsto\:f(x) = 1 - |x - 2|$

Now, We know that

Domain is defined as set of those real values of 'x' where f(x) is well defined.

Clearly, we observe that f(x) is defined for all real values of x.

So,

$\bf\implies \:Domain \: of \: f (x) \: is \:defined \: \forall \: x \in \: R$

Now, To find the range of f(x).

Range is defined as set of all real values of x taken by f(x) on its domain.

Now, Given function is

$\rm :\longmapsto\:f(x) = 1 - |x - 2|$

We know,

$\red{\rm :\longmapsto\: |x - 2| \geqslant 0}$

So,

$\red{\rm :\longmapsto\: - |x - 2| \leqslant 0}$

On adding 1 on both sides,

$\red{\rm :\longmapsto\: 1 - |x - 2| \leqslant 0 + 1}$

$\red{\rm \implies\:f(x) \leqslant 1}$

$\red{\rm \implies\:Range \: of \: f(x) \: is \: ( - \infty , \: 1] \: }$

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Additional Information :-

$\boxed{ \tt{ \: x > y \: \: \rm \implies\: - x < - y \: }}$

$\boxed{ \tt{ \: x < y \: \: \rm \implies\: - x > - y \: }}$

$\boxed{ \tt{ \: x \geqslant y \: \: \rm \implies\: - x \leqslant - y \: }}$

$\boxed{ \tt{ \: x \leqslant y \: \: \rm \implies\: - x \geqslant - y \: }}$

$\boxed{ \tt{ \: |x| < y \: \: \rm \implies\: - y < x < y \: }}$

$\boxed{ \tt{ \: |x| \leqslant y \: \: \rm \implies\: - y \leqslant x \leqslant y \: }}$

$\boxed{ \tt{ \: |x| > y \: \: \rm \implies\:x < - y \: or \: x > y \: }}$

$\boxed{ \tt{ \: |x| \geqslant y \: \: \rm \implies\:x \leqslant - y \: or \: x \geqslant y \: }}$

$\boxed{ \tt{ \: |x - z| < y \: \: \rm \implies\:z - y < x < z + y \: }}$

$\boxed{ \tt{ \: |x - z| \leqslant y \: \: \rm \implies\:z - y \leqslant x \leqslant z + y \: }}$

Answer 2

Step-by-step explanation:

Domain = All real numbers.

Range of f(x) : is f(x) is less than or equals to 1