Question

the range of the function f(x)=|x-1|+2​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• Range of f(x) is $[2, \infty)$

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Here,

$\:\:\:\:\:\:\:\:\:\:\: - \infty < x < \infty$

$\implies - \infty < x - 1 < \infty$

$\implies 0 ≤ |x - 1| < \infty$

$\implies 2 ≤ |x - 1| + 2 < \infty$

$\implies 2 ≤ f(x) < \infty$

$\implies f(x) ∈ [2, \infty)$

Hence, range of f(x) is $[2, \infty).$