Let and , which one of the following is/are…

MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions

Problem

Let f(x)={x2−4x+3,x<3x−4,x≥3f(x) = \begin{cases} x^2 - 4x + 3, & x < 3 \\ x - 4, & x \ge 3 \end{cases} and g(x)={x−3,x<4x2+2x+2,x≥4g(x) = \begin{cases} x - 3, & x < 4 \\ x^2 + 2x + 2, & x \ge 4 \end{cases} , which one of the following is/are true? (1) (f+g)(3.5)=0(f+g)(3.5) = 0 (2) f(g(3))=3f(g(3)) = 3 (3) f(g(2))=1f(g(2)) = 1 (4) (f−g)(4)=0(f-g)(4) = 0

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