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Let and , which one of the following is/are…
MATHEMATICS · Single correct · AoPS · Mathematics · Functions · Functions
Problem Let f ( x ) = { x 2 − 4 x + 3 , x < 3 x − 4 , x ≥ 3 f(x) = \begin{cases} x^2 - 4x + 3, & x < 3 \\ x - 4, & x \ge 3 \end{cases} f ( x ) = { x 2 − 4 x + 3 , x − 4 , x < 3 x ≥ 3
and g ( x ) = { x − 3 , x < 4 x 2 + 2 x + 2 , x ≥ 4 g(x) = \begin{cases} x - 3, & x < 4 \\ x^2 + 2x + 2, & x \ge 4 \end{cases} g ( x ) = { x − 3 , x 2 + 2 x + 2 , x < 4 x ≥ 4 , which one of the
following is/are true?
(1) ( f + g ) ( 3.5 ) = 0 (f+g)(3.5) = 0 ( f + g ) ( 3.5 ) = 0
(2) f ( g ( 3 ) ) = 3 f(g(3)) = 3 f ( g ( 3 )) = 3
(3) f ( g ( 2 ) ) = 1 f(g(2)) = 1 f ( g ( 2 )) = 1
(4) ( f − g ) ( 4 ) = 0 (f-g)(4) = 0 ( f − g ) ( 4 ) = 0
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