Question

f(x) =|x^2-4|+4. Determinați imaginea funcției. f:R->R

Answer 1

f(x) =|x²-4|+4; f:R->R

|x²-4|≥0

=> f(x)≥4

=>  Imf=[4;+∞)

Answer 2

$f:\mathbb{R}\rightarrow \mathbb{R},$

$f(x) = |x^2-4|+4 \\ \\ |x^2-4| \geq 0\Big|+4 \Rightarrow |x^2-4|+4\geq 4 \Rightarrow f(x) \geq 4 \\ \\ \Rightarrow\boxed{Imf = [4,+\infty)}$