Let 𝑓, 𝑔∶ℝ → ℝ be defined by 𝑓(𝑥)={ 𝑥+2, 2𝑥+1, 𝑥≤1 𝑥... | Mathematics for Economy | SolveeIt | Solveeit

Today, August 23

Question

Let 𝑓, 𝑔∶ℝ → ℝ be defined by
𝑓𝑥={ 𝑥+2, 2𝑥+1, 𝑥≤1 𝑥>1 and 𝑔𝑥 = { 2𝑥, 𝑥 + 2, 𝑥 ≤ 2 𝑥 > 2.
Then

A

𝑓 is convex and 𝑔 is concave

B

𝑓 is concave and 𝑔 is convex

C

both 𝑓 and 𝑔 are concave

D

both 𝑓 and 𝑔 are convex

Answer

𝑓 is convex and 𝑔 is concave

Explanation

Solution

The correct option is (A): 𝑓 is convex and 𝑔 is concave