Prove Convexity of Set Defined by x^2 ≤ a

Math Problem Statement

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Convex Sets
Inequalities
Real Analysis

Convexity condition: f(λx + (1−λ)y) ≤ λf(x) + (1−λ)f(y)
Set definition: S = {x ∈ R : x^2 ≤ a}

Convex Set Definition
Jensen's Inequality

Undergraduate Mathematics

Proving the Convexity of the Set x^2 + y^2 ≤ 5

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Show that the Set S = { x | |x| <= 2 } is Convex

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Proof of |x| ≤ a iff -a ≤ x ≤ a for a ≥ 0