Question

Find the range of the following functions given by f(x) = 1 – |x – 2| 

Answer 1

For real value of f

|x – 2| ≥ 0

Adding negative sign, we get

Or –|x – 2| ≤ 0

Adding 1 we get

⇒ 1 – |x – 2| ≤ 1

Or f(x) ≤ 1

⇒ f(x) ∈ `(–oo, 1]`

Therefore, the range of f = `(–oo, 1]`