Find the range of the following functions given by

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

To find: the range of function

Explanation: So, the range of a function consists of all the second elements of all the ordered pairs, i.e., f(x), so we have to find the values of f(x) to get the required range

Given,

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

Now 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)∈ (-∞, 1]

Hence the range of f = (-∞, 1]