Question

f(x)=|x-2|+|x+2|
Find range of following function
(plz answer right) ​

Answer 1

Answer:

Range of the fuction is [4, ∞).

Step-by-step explanation:

f(x) = |x-2| + |x+2|

= - (x-2) - (x+2) , x ≤ - 2

f(x) = - (x-2) + (x+2) , -2 ≤ x ≤ 2

= (x-2) + (x+2) , x ≥ 2

= - 2x, x ≤ -2

f(x) = 4 , -2 ≤ x ≤ 2

= 2x , x ≥ 2

when x ≤ -2

so, x ≤ -2

⇒ 2x ≤ -4

⇒ -2x ≥ 4

⇒ f(x) ≥ 4

when -2 ≤ x ≤ 2

f(x) = 4

when x ≥ 2

So, x ≥ 2

or 2x ≥ 4

or f(x) ≥ 4

Hence, 4 ≤ f(x) < ∞

or f(x) ∈ [4, ∞)

Therefore, Range of f(x) is [4, ∞).