Let-f-x-x-2-x-4-2x-6-for-2-x-8-The-sum-of-the-largest-and-smallest-values-of-f-x-is-

Question Number 110359 by Aina Samuel Temidayo last updated on 28/Aug/20

Let

f (x) =∣ x - 2 ∣ + ∣ x - 4 ∣ - ∣ 2 x - 6 ∣,

for 2 ⩽ x ⩽ 8 . The sum of

the largest and

smallest values of f (x) is

Answered by bobhans last updated on 28/Aug/20

∣ x - 2 ∣ = {\begin{cases} x - 2; x ⩾ 2 \\ - x + 2; x < 2 \end{cases}

∣ x - 4 ∣ = {\begin{cases} x - 4; x ⩾ 4 \\ - x + 4; x < 4 \end{cases}

∣ 2 x - 6 ∣ = {\begin{cases} 2 x - 6; x ⩾ 3 \\ - 2 x + 6; x < 3 \end{cases}

g i v e n 2 ⩽ x ⩽ 8 \to 2 ⩽ x < 3 \cup 3 ⩽ x < 4 \cup 4 ⩽ x ⩽ 8

c a s e (1) 2 ⩽ x < 3 \to f (x) = x - 2 - (x - 4) + 2 x - 6

f (x) = 2 x - 4 \to {\begin{cases} f (2) = 0 \\ f (3) = 2 \end{cases}

c a s e (2) 3 ⩽ x < 4 \to f (x) = x - 2 - (x - 4) - (2 x - 6)

f (x) = - 2 x + 8 \to {\begin{cases} f (3) = 2 \\ f (4) = 0 \end{cases}

c a s e (3) 4 ⩽ x ⩽ 8 \to f (x) = x - 2 + x - 4 - (2 x - 6)

f (x) = 0

m i n v a l u e o f f (x) = 0 & m a x v a l u e o f

f (x) = 2

Σ (m i n, m a x) = 2

Commented by Aina Samuel Temidayo last updated on 28/Aug/20

Wow . Thanks . Please help in the

remaining questions I posted .

Commented by Aina Samuel Temidayo last updated on 28/Aug/20

Please how did you get this : given

2 ⩽ x ⩽ 8 \to 2 ⩽ x < 3 \cup 3 ⩽ x < 4 \cup 4 ⩽ x ⩽ 8