Find the maximum and the minimum values (if any) of the function $f(x)=-|x-2|+5$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Maximum value: 5; Minimum value: None
Given $f(x) = −|x-2|+5, D_f= R$.
As $|x-2|≥ 0$ for all $x ∈ R⇒-|x-2|≤0$ for all $x ∈ R$
$⇒-|x-2|+5≤5$ for all $x ∈ R$.
Therefore, the maximum value of f(x) is 5, it has no minimum value.